International Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-190110820170806Fixed point theorems in modular vector spaces40464057http://dx.doi.org/10.22436/jnsa.010.08.01ENAfrah A. N.AbdouDepartment of Mathematics, Faculty of Sciences, King Abdulaziz University, Jeddah 21593, Saudi Arabia.Mohamed A.KhamsiDepartment of Mathematical Sciences, The University of Texas at El Paso, El Paso, TX 79968, U.S.A.In this work, we initiate the metric fixed point theory in modular vector spaces under Nakano formulation. In particular, we
establish an analogue to Banach contraction principle, Browder and G¨ohde fixed point theorems for nonexpansive mappings in
the modular sense. Then we finish by proving a common fixed point result of a commutative family of nonexpansive mappings
in the modular sense.
http://isr-publications.com/jnsa/5185/download-fixed-point-theorems-in-modular-vector-spacesInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-190110820170806Skew cyclic displacements and decompositions of inverse matrix for an innovative structure matrix40584070http://dx.doi.org/10.22436/jnsa.010.08.02ENXiaoyuJiangDepartment of Information and Telecommunications Engineering, The University of Suwon, Wau-ri, Bongdam-eup, Hwaseong-si, Gyeonggi-do, 445-743, Korea.KicheonHongDepartment of Information and Telecommunications Engineering, The University of Suwon, Wau-ri, Bongdam-eup, Hwaseong-si, Gyeonggi-do, 445-743, Korea.ZunweiFuDepartment of Mathematics, The University of Suwon, Wau-ri, Bongdam-eup, Hwaseong-si, Gyeonggi-do, 445-743, Korea. In this paper, we study mainly on a class of column upper-minus-lower (CUML) Toeplitz matrices without standard Toeplitz structure, which are `` similar'' to the Toeplitz matrices. Their (-1,-1)-cyclic displacements coincide with cyclic displacement of some standard Toeplitz matrices. We obtain the formula on representation for the inverses of CUML Toeplitz matrices in the form of sums of products of (-1, 1)-circulants and (1, -1)-circulants factor by constructing the corresponding displacement of the matrices. In addition, based on the relation between CUML Toeplitz matrices and CUML Hankel matrices, the inverse formula of CUML Hankel matrices can also be obtained.
http://isr-publications.com/jnsa/5186/download-skew-cyclic-displacements-and-decompositions-of-inverse-matrix-for-an-innovative-structure-matrixInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-190110820170806On approximate homomorphisms of ternary semigroups40714076http://dx.doi.org/10.22436/jnsa.010.08.03ENKrzysztofCieplińskiAGH University of Science and Technology, Faculty of Applied Mathematics, Mickiewicza 30, 30-059 Krakow, Poland.We prove the generalized Ulam stability of ternary homomorphisms from commutative ternary semigroups into \(n\)-Banach spaces as well as into complete non-Archimedean normed spaces. Ternary algebraic structures appear in various domains of theoretical and mathematical physics, and \(p\)-adic numbers, which are the most important examples of non-Archimedean fields, have gained the interest of physicists for their research in some problems coming from quantum physics, \(p\)-adic strings and superstrings.
http://isr-publications.com/jnsa/5187/download-on-approximate-homomorphisms-of-ternary-semigroupsInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-190110820170806On the generalized solutions of a certain fourth order Euler equations40774084http://dx.doi.org/10.22436/jnsa.010.08.04ENAmphonLiangpromDepartment of Mathematics, Khon Kaen University, Khon Kaen 40002, Thailand.KamsingNonlaoponDepartment of Mathematics, Khon Kaen University, Khon Kaen 40002, Thailand. In this paper, using Laplace transform technique, we propose the generalized solutions of the fourth order Euler differential equations \[t^4y^{(4)}(t)+t^3y'''(t)+t^2y''(t)+ty'(t)+my(t)=0,\] where \(m\) is an integer and \(t\in\mathbb{R}\). We find types of solutions depend on the values of \(m\). Precisely, we have a distributional solution for \(m=-k^4-5k^3-9k^2-4k\) and a weak solution for \(m=-k^4+5k^3-9k^2+4k,\) where \(k\in\mathbb{N}.\)
http://isr-publications.com/jnsa/5188/download-on-the-generalized-solutions-of-a-certain-fourth-order-euler-equationsInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-190110820170807On some common coupled fixed point results in rectangular \(b\)-metric spaces40854098http://dx.doi.org/10.22436/jnsa.010.08.05ENFengGuInstitute of Applied Mathematics and Department of Mathematics, Hangzhou Normal University, Hangzhou, Zhejiang 310036, China. In this paper, by using the \(w\)-compatible conditions of mapping pair, we discuss the existence and uniqueness problem of the common coupled fixed point for mappings defined on a set equipped with two rectangular \(b\)-metrics. Some new common coupled fixed point theorems are obtained. We also provide
illustrative examples in support of our new results. As application, we provide an existence and uniqueness theorem of common solution for a class of nonlinear integral equations by using the obtained new result. The results presented in this paper generalize the well-known comparable results in the literature.
http://isr-publications.com/jnsa/5195/download-on-some-common-coupled-fixed-point-results-in-rectangular-b-metric-spacesInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-190110820170807Weak convergence of an iterative algorithm for accretive operators 40994108http://dx.doi.org/10.22436/jnsa.010.08.06ENHengjunZhaoSchool of Science, Henan University of Engineering, Zhengzhou 451191, China.Sun YoungChoCenter for General Education, China Medical University, Taichung, Taiwan. In this paper, an iterative algorithm investigated for \(m\)-accretive and inverse-strongly accretive operators. Also, a weak convergence theorem for the sum of two accretive operators is established in a real uniformly convex and \(q\)-uniformly
smooth Banach space.http://isr-publications.com/jnsa/5196/download-weak-convergence-of-an-iterative-algorithm-for-accretive-operatorsInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-190110820170807Relaxed inertial accelerated algorithms for solving split equality feasibility problem41094121http://dx.doi.org/10.22436/jnsa.010.08.07ENMeixiaLiSchool of Mathematics and Information Science, Weifang University, Weifang, 261061, China.XipingKaoCollege of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao, 266590, China.HaitaoCheSchool of Mathematics and Information Science, Weifang University, Weifang, 261061, China.In this paper, we study the split equality feasibility problem and present two algorithms for solving the problem with special structure. We prove the weak convergence of these algorithms under mild conditions. Especially, the selection of stepsize is only dependent on the information of current iterative points, but independent from the prior knowledge of operator norms. These algorithms provide new ideas for solving the split equality feasibility problem. Numerical results demonstrate the feasibility and effectiveness of these algorithms.
http://isr-publications.com/jnsa/5197/download-relaxed-inertial-accelerated-algorithms-for-solving-split-equality-feasibility-problemInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-190110820170809Second-order accurate numerical approximations for the fractional percolation equations41224136http://dx.doi.org/10.22436/jnsa.010.08.08ENXiucaoYinDepartment of Mathematics, South China Agricultural University, Guangzhou 510640, P. R. China.LangLiDepartment of Mathematics, South China Agricultural University, Guangzhou 510640, P. R. China.ShaomeiFangDepartment of Mathematics, South China Agricultural University, Guangzhou 510640, P. R. China.First, we examine a practical numerical method which based on the classical Crank-Nicholson (CN) method combined with Richardson extrapolation is used to solve a class of one-dimensional initial-boundary value fractional percolation equation (FPE) with variable coefficients on a finite domain. Secondly, we present ADI-CN method for the two-dimensional fractional percolation equation. Stability and convergence of these methods are proved. Using these methods, we can achieve second-order convergence in time and space. Finally, numerical examples are presented to verify the order of convergence.
http://isr-publications.com/jnsa/5208/download-second-order-accurate-numerical-approximations-for-the-fractional-percolation-equationsInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-190110820170809Some identities of \(\lambda\)-Daehee polynomials41374142http://dx.doi.org/10.22436/jnsa.010.08.09ENJeong GonLeeDivision of Mathematics and informational Statistics, Nanoscale Science and Technology Institute, Wonkwang University, Iksan, 570-749, Republic of Korea.JongkyumKwonDepartment of Mathematics Education and RINS, Gyeongsang National University, Jinju, Gyeongsangnamdo, 52828, Republic of Korea.Gwan-WooJangDepartment of Mathematics, Kwangwoon University, Seoul, 139-701, Republic of Korea.Lee-ChaeJangGraduate school of Education, Konkuk University, Seoul, 143-701, Republic of Korea.In this paper, we give some identities of \(\lambda\)-Daehee polynomials and investigate a new and interesting identities of \(\lambda\)-Daehee polynomial arising from the symmetry properties of the \(p\)-adic invariant integral on \(\mathbb{Z}_p\).http://isr-publications.com/jnsa/5209/download-some-identities-of-lambda-daehee-polynomialsInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-190110820170810Convergence analysis of a Halpern-like iterative algorithm in Hilbert spaces41434149http://dx.doi.org/10.22436/jnsa.010.08.10ENYunpengZhangCollege of Electric Power, North China University of Water Resources and Electric Power, Zhengzhou 450011, China.Sun YoungChoCenter for General Education, China Medical University, Taichung 40402, Taiwan. In this paper, a Halpern-like iterative algorithm is investigated for finding a solution of a split feasibility problem and a solution to a nonexpansive operator equation. Strong convergence theorems are established in the framework of infinite dimensional Hilbert spaces.
http://isr-publications.com/jnsa/5226/download-convergence-analysis-of-a-halpern-like-iterative-algorithm-in-hilbert-spacesInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-190110820170810Some properties and mappings on weakly \(\nu \)-Lindelöf generalized topological spaces41504161http://dx.doi.org/10.22436/jnsa.010.08.11ENM.AbuageInstitute for Mathematical Research, University Putra Malaysia, 43400 UPM, Serdang, Selangor, Malaysia.A.KılıçmanDepartment of Mathematics, University Putra Malaysia, 43400 UPM, Serdang, Selangor, Malaysia. Our work aims to study weakly \(\nu \)-Lindelöf (briefly \(w\nu \)-Lindelöf) space in generalized topological spaces. Some characterizations of \(w\nu \)-Lindelöf subspaces and subsets are showed.
Furthermore, we shall show that the \(w\nu \)-Lindelöf generalized topological space is not a hereditary property. Finally, the effect of some mappings and decompositions of continuity are studied. The main result that we obtained on is the effect of almost \((\nu, \mu)\)-continuous function on \(w\nu \)-Lindelöf generalized topological space.
http://isr-publications.com/jnsa/5228/download-some-properties-and-mappings-on-weakly-nu-lindelof-generalized-topological-spacesInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-190110820170811Some applications with new admissibility contractions in \(b\)-metric spaces41624174http://dx.doi.org/10.22436/jnsa.010.08.12ENLjiljanaPaunovićUniversity of Priˇstina-Kosovska Mitrovica, Teacher Education School in Prizren-Leposavi´c, 38218 Leposavi´c, Serbia.PreetiKaushikDepartment of Mathematics, DCRUST, Murthal, Sonepat 131039, India.SanjayKumarDepartment of Mathematics, DCRUST, Murthal, Sonepat 131039, India.The work presented in this paper extends the idea of \(\alpha-\beta\)-contractive mappings in the framework of \(b\)-metric spaces. Fixed points are investigated for such kind of mappings. An example is given to show the superiority of our results. As applications we discuss Ulam-Hyres stability, well-posedness
and limit shadowing of fixed point problem.
http://isr-publications.com/jnsa/5230/download-some-applications-with-new-admissibility-contractions-in-b-metric-spacesInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-190110820170811Lie group method and fractional differential equations41754180http://dx.doi.org/10.22436/jnsa.010.08.13ENM. M.AlshamraniDepartment of Mathematics, Faculty of Science, Northern Border University, Arar, Saudi Arabia.H. A.ZedanDepartment of Mathematics, Faculty of Science, Kafrelsheikh University, Egypt.M.Abu-NawasDepartment of Mathematics, Faculty of Science, Northern Border University, Arar, Saudi Arabia.In this paper, Lie group method is applied to investigate and solve
some classes of nonlinear fractional differential equations. In
addition, we use the obtained symmetries to induce exact solutions for the equations under consideration.
http://isr-publications.com/jnsa/5231/download-lie-group-method-and-fractional-differential-equationsInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-190110820170813Hopf bifurcation analysis and its preliminary control in a Hasting-Powell food chain model with two different delays41814196http://dx.doi.org/10.22436/jnsa.010.08.14ENJiangangZhangSchool of Mathematics and Physics, Lanzhou Jiaotong University, Lanzhou 730070, China.JiarongLuSchool of Mathematics and Physics, Lanzhou Jiaotong University, Lanzhou 730070, China.WenjuDuSchool of Traffic and Transportation, Lanzhou Jiaotong University, Lanzhou 730070, China.YandongChuSchool of Mathematics and Physics, Lanzhou Jiaotong University, Lanzhou 730070, China.HongweiLuoSchool of Mathematics and Physics, Lanzhou Jiaotong University, Lanzhou 730070, China.Keeping the balance of nature is important, and it is very significant to effectively control the number of species for ecosystem stability. In this paper, we propose a tritrophic Hastings-Powell (HP) model with two different time delays, and the local stability of equilibrium, Hopf bifurcation, and the existence and uniqueness of the positive equilibrium are analyzed in detail. Besides, we obtain the stable conditions for the system and prove that Hopf bifurcation will occur when the delay pass through the critical value. And the stability and direction of the Hopf bifurcation are also investigated by using the center manifold theorem and normal form theorem. Finally, some numerical examples are given to illustrate the results.
http://isr-publications.com/jnsa/5254/download-hopf-bifurcation-analysis-and-its-preliminary-control-in-a-hasting-powell-food-chain-model-with-two-different-delaysInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-190110820170813Fixed point results for generalized \((\alpha-\eta)-\Theta\) contractions with applications41974208http://dx.doi.org/10.22436/jnsa.010.08.15ENNawabHussainDepartment of Mathematics, King Abdulaziz University, P. O. Box 80203, Jeddah 21589, Saudi Arabia.Abdullah EqalAl-MazrooeiDepartment of Mathematics, University of Jeddah, P .O. Box 80327, Jeddah 21589, Saudi Arabia.JamshaidAhmadDepartment of Mathematics, University of Jeddah, P .O. Box 80327, Jeddah 21589, Saudi Arabia. The aim of this paper is to define
generalized \((\alpha-\eta)-\Theta\) contraction and to extend the results of Jleli and Samet [M. Jleli, B. Samet, J. Inequal. Appl., \(\bf{2014}\) (2014), 8 pages] by applying a simple condition on the function \(\Theta\). We also deduce certain fixed and
periodic point results for orbitally continuous generalized \(\Theta \)-contractions and certain fixed point results for integral inequalities are derived. Finally, we provide an example to show the significance of the
investigation of this paper.
http://isr-publications.com/jnsa/5256/download-fixed-point-results-for-generalized-alpha-eta-theta-contractions-with-applicationsInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-190110820170816Global well-posedness of strong solution for the three dimensional dynamic Cahn-Hilliard-Stokes model42094221http://dx.doi.org/10.22436/jnsa.010.08.16ENKelongChengSchool of Science, Southwest University of Science and Technology, Mianyang, Sichuan 621010, China.WenqiangFengDepartment of Mathematics, University of Tennessee, Knoxville, Tennessee 37996, USA. The global well-posedness analysis for the three dimensional dynamic Cahn-Hilliard-Stokes (CHS) model is provided in this paper. In this model, the velocity vector is determined by the phase variable by both the Darcy law and the Stokes equation. Based on the analysis of weak solutions to the CHS equation by the standard Galerkin method, we present a global in time strong solution for the CHS model. Moreover, the existence and the uniqueness of the strong solution are also proven.
http://isr-publications.com/jnsa/5280/download-global-well-posedness-of-strong-solution-for-the-three-dimensional-dynamic-cahn-hilliard-stokes-modelInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-190110820170816Optimal harvesting policy of a stochastic delay predator-prey model with Lévy jumps42224230http://dx.doi.org/10.22436/jnsa.010.08.17ENMeilingDengSchool of Mathematical Science, Huaiyin Normal University, Huaian 223300, P. R. China.This paper considers the optimal harvesting of a stochastic delay predator-prey model with Lévy jumps. The traditional optimal harvesting problem of this type of model is difficult because it is difficult to get the explicit solutions of the model or to solve the corresponding delay Fokker-Planck equation of the model. In this paper, we use an ergodic method to study this problem, and establish the sufficient and necessary conditions for the existence of an optimal harvesting strategy of the model. In addition, we gain the explicit forms of the optimal harvesting effort and the maximum of the cost function. One can see that the ergodic method used in this paper can avoid solving both the model and the corresponding delay Fokker-Planck equation.
http://isr-publications.com/jnsa/5281/download-optimal-harvesting-policy-of-a-stochastic-delay-predator-prey-model-with-levy-jumpsInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-190110820170816New numerical analysis of Riemann-Liouville time-fractional Schrödinger with power, exponential decay, and Mittag-Leffler laws42314243http://dx.doi.org/10.22436/jnsa.010.08.18ENBadr Saad T.AlkahtaniDepartment of mathematics, colle of science, King Saud University, P. O. Box 1142, Riyadh 11989, Saudi Arabia.IlknurKocaDepartment of Mathematics, Faculty of Sciences, Mehmet Akif Ersoy University, 15100, Burdur, Turkey.AbdonAtanganaInstitute for Groundwater Studies, Faculty of Natural and Agricultural Sciences, University of the Free State, 9300, Bloemfontein, South Africa. The mathematical equation that describes how the quantum state of a quantum system changes during time was considered within the framework of fractional differentiation with three
different derivatives in Riemann-Liouville sense. The fractional derivatives used in this work are constructed based on power, exponential decay, and Mittag-Leffler law. A new numerical scheme for fractional derivative in Riemann-Liouville sense is presented and used to solve numerically the Schrödinger equation. The stability analysis of each model is presented in
detail.
http://isr-publications.com/jnsa/5282/download-new-numerical-analysis-of-riemann-liouville-time-fractional-schrodinger-with-power-exponential-decay-and-mittag-leffler-lawsInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-190110820170820The extended Mittag-Leffler function via fractional calculus42444253http://dx.doi.org/10.22436/jnsa.010.08.19ENGauharRahmanDepartment of Mathematics, International Islamic University, Islamabad, PakistanDumitruBaleanuDepartment of Mathematics, Cankaya University, Ankara, Turkey and Institute of Space Sciences, Magurele-Bucharest, Romania Maysaa AlQurashiDepartment of Mathematics, College of Science, King Saud University, Riyadh, Saudia ArabiaSunil DuttPurohitDepartment of HEAS (Mathematics), Rajasthan Technical University, Kota, IndiaShahidMubeenDepartment of Mathematics, University of Sargodha, Sargodha, PakistanMuhammadArshadDepartment of Mathematics, International Islamic University, Islamabad, Pakistan In this study, our main attempt is to introduce fractional calculus (fractional integral and differential) operators which contain the following new family of extended Mittag-Leffler function:
\[
E_{\alpha,\beta}^{\gamma;q, c}(z)=\sum\limits_{n=0}^{\infty}\frac{B_p(\gamma+nq, c-\gamma)(c)_{nq}}{B(\gamma, c-\gamma)\Gamma(\alpha n+\beta)}\frac{z^n}{n!},~~~ (z,\beta, \gamma\in\mathbb{C}),
\]
as its kernel. We also investigate a certain number of their consequences containing the said function in their kernels.
http://isr-publications.com/jnsa/5310/download-the-extended-mittag-leffler-function-via-fractional-calculusInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-190110820170820Viscosity approximation methods for the multiple-set split equality common fixed-point problems of demicontractive mappings42544268http://dx.doi.org/10.22436/jnsa.010.08.20ENYaqin WangDepartment of Mathematics, Shaoxing University, Shaoxing 312000, ChinaXiaoli FangDepartment of Mathematics, Shaoxing University, Shaoxing 312000, China In this paper, we consider a new parallel algorithm combining viscosity approximation methods to approximate the multiple-set split common fixed point problem governed by demicontractive mappings, and get the generated sequence converges strongly to a solution of this problem.
The results obtained in this paper generalize and improve the recent ones announced by many others.
http://isr-publications.com/jnsa/5311/download-viscosity-approximation-methods-for-the-multiple-set-split-equality-common-fixed-point-problems-of-demicontractive-mappingsInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-190110820170820Essential norm of a product-type operator from Bergman space to weighted-type space42694274http://dx.doi.org/10.22436/jnsa.010.08.21ENYa-Song ChenDepartment of Mathematics, Tianjin Polytechnic University, Tianjin 300160, P. R. ChinaZhong-Shan FangDepartment of Mathematics, Tianjin Polytechnic University, Tianjin 300160, P. R. ChinaYeong-Cheng LiouDepartment of Healthcare Administration and Medical Informatics, Center for Big Data Analytics and Intelligent Healthcare, and Research Center of Nonlinear Analysis and Optimization, Kaohsiung Medical University, Kaohsiung 807, Taiwan In this paper, we discuss the boundedness of a product-type operator
introduced by Stević, which acting from Bergman space to the
weighted-type spaces or the little weighted-type spaces in the unit
ball, and characterize the the essential norm of the product-type
operator. From which the sufficient and necessary condition of
compactness of this type operator follows immediately.
http://isr-publications.com/jnsa/5312/download-essential-norm-of-a-product-type-operator-from-bergman-space-to-weighted-type-spaceInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-190110820170822A version of the Stone-Weierstrass theorem in fuzzy analysis42754283http://dx.doi.org/10.22436/jnsa.010.08.22ENJuan J.FontDepartament de Matemàtiques, and Institut Universitari de Matemàtiques i Aplicacions de Castelló (IMAC), Universitat Jaume I, Campus del Riu Sec. s/n, 12071 Castelló, SpainDelia SanchisDepartament de Matemàtiques, and Institut Universitari de Matemàtiques i Aplicacions de Castelló (IMAC), Universitat Jaume I, Campus del Riu Sec. s/n, 12071 Castelló, SpainManuelSanchisDepartament de Matemàtiques, and Institut Universitari de Matemàtiques i Aplicacions de Castelló (IMAC), Universitat Jaume I, Campus del Riu Sec. s/n, 12071 Castelló, Spain Let \(C(K,\mathbb{E}^1)\) be the space of continuous functions defined between a compact Hausdorff space \(K\) and the space of fuzzy numbers \(\mathbb{E}^1\) endowed with the supremum metric.
We provide a set of sufficient conditions on a subspace of \(C(K,\mathbb{E}^1)\) in order that it be dense. We also obtain a similar result for interpolating families of \(C(K,\mathbb{E}^1)\).
As a corollary of the above results we prove that certain fuzzy-number-valued neural networks can approximate any continuous fuzzy-number-valued function defined on a compact subspace of \(\mathbb{R}^n\).
http://isr-publications.com/jnsa/5327/download-a-version-of-the-stone-weierstrass-theorem-in-fuzzy-analysisInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-190110820170822Generalized convolution properties based on the modified Mittag-Leffler function42844294http://dx.doi.org/10.22436/jnsa.010.08.23ENH. M. SrivastavaDepartment of Mathematics and Statistics, University of Victoria, Victoria, British Columbia V8W 3R4, CanadaAdemKılıçmanDepartment of Mathematics, Universiti Putra Malaysia, 43400 UPM Serdang, Selangor, MalaysiaZainab E. AbdulnabyDepartment of Mathematics, College of Science, Al-Mustansiriyah University, Baghdad, IraqRabha W. Ibrahimaculty of Computer Science and Information Technology, University of Malaya, 50603 Kuala Lumpur, Malaysia Studies of convolution play an important role in Geometric Function
Theory (GFT). Such studies attracted a large number of researchers in recent years. By
making use of the Hadamard product (or convolution), several new and interesting subclasses
of analytic and univalent functions have been introduced and investigated in the direction of well-known
concepts such as the subordination and superordination inequalities,
integral mean and partial sums, and so on. In this article, we apply the
Hadamard product (or convolution) by utilizing some special
functions. Our contribution in this paper includes defining a new linear operator in the
form of the generalized Mittag-Leffler function in terms of the
extensively-investigated Fox-Wright \(\:_p\Psi_q\)-function in the right-half of the open unit disk where where \(\Re(z)>0.\) We then show that the new linear convolution operator is bounded in some spaces.
In particular, several boundedness properties of this linear convolution operator under mappings from a weighted Bloch space into a weighted-log Bloch space are also investigated. For uniformity and convenience, the Fox-Wright \(\:_p\Psi_q\)-notation is used in our results.
http://isr-publications.com/jnsa/5328/download-generalized-convolution-properties-based-on-the-modified-mittag-leffler-functionInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-190110820170822Boundedness of high order commutators of Marcinkiewicz integrals associated with Schrödinger operators42954306http://dx.doi.org/10.22436/jnsa.010.08.24ENHui WangTeachers College, Nanyang Institute of Technology, Nanyang, 473000, P. R. ChinaBijun RenDepartment of Information Engineering, Henan Institute of Finance and Banking, Zhengzhou, 451464, P. R. China Suppose \(L=-\Delta+V\) is a Schrödinger operator on \(\mathbb{R}^n\), where \(n\geq 3\)
and the nonnegative potential \(V\) belongs to reverse Hölder class \(RH_{n}.\) Let \(b\) belong to a new Campanato space \(\Lambda_\beta^\theta(\rho),\) and let \(\mu_j^L\) be the Marcinkiewicz integrals associated with \(L.\) In this paper, we establish the boundedness of the \(m\)-order commutators \([b^m, \mu_j^L]\) from \(L^p(\mathbb{R}^n)\) to \(L^q(\mathbb{R}^n),\) where
\(1/q=1/p-m\beta/n\) and \(1<p<n/(m\beta).\) As an application, we obtain the boundedness of \([b^m, \mu_j^L]\) on the generalized Morrey spaces
related to certain nonnegative potentials.
http://isr-publications.com/jnsa/5329/download-boundedness-of-high-order-commutators-of-marcinkiewicz-integrals-associated-with-schrodinger-operatorsInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-190110820170822A coincidence-point problem of Perov type on rectangular cone metric spaces43074317http://dx.doi.org/10.22436/jnsa.010.08.25ENFairouz TchierMathematics Department College of Science (Malaz), King Saud University, P. O. Box 22452, Riyadh, King Saudi ArabiaCalogero VetroDepartment of Mathematics and Computer Science, University of Palermo, Via Archirafi 34, 90123 Palermo, ItalyFrancescaVetroDepartment of Energy, Information Engineering and Mathematical Models (DEIM), University of Palermo, Viale delle Scienze, 90128 Palermo, ItalyWe consider a coincidence-point problem in the setting of rectangular cone metric spaces. Using \(\alpha\)-admissible mappings and following Perov's approach, we establish some existence and uniqueness results for two self-mappings. Under a compatibility assumption, we also solve a common fixed-point problem.
http://isr-publications.com/jnsa/5330/download-a-coincidence-point-problem-of-perov-type-on-rectangular-cone-metric-spacesInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-190110820170824Well-posedness for systems of time-dependent hemivariational inequalities in Banach spaces43184336http://dx.doi.org/10.22436/jnsa.010.08.26ENLu-Chuan CengDepartment of Mathematics, Shanghai Normal University, Shanghai 200234, China. Yeong-Cheng LiouDepartment of Healthcare Administration and Medical Informatics, Center for Big Data Analytics and Intelligent Healthcare, and Research Center of Nonlinear Analysis and Optimization, Kaohsiung Medical University, Kaohsiung 807, Taiwan.Jen-Chih YaoCenter for General Education, China Medical University, Taichung 40402, TaiwanYonghong YaoDepartment of Mathematics, Tianjin Polytechnic University, Tianjin 300387, ChinaIn this paper, we generalize the concept of \(\alpha\)-well-posedness to a system of time-dependent hemivariational inequalities without Volterra integral terms in Banach spaces. We establish some metric characterizations of \(\alpha\)-well-posedness and prove some equivalence results of strong \(\alpha\)-well-posedness (resp., in the generalized sense) between a system of time-dependent hemivariational inequalities and its derived system of inclusion problems.
http://isr-publications.com/jnsa/5342/download-well-posedness-for-systems-of-time-dependent-hemivariational-inequalities-in-banach-spacesInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-190110820170824A general iterative algorithm for vector equilibrium problem43374351http://dx.doi.org/10.22436/jnsa.010.08.27ENJin-xia HuangDepartment of Mathematics, Nanchang University, Nanchang, Jiangxi 330031, ChinaSan-hua WangDepartment of Mathematics, Nanchang University, Nanchang, Jiangxi 330031, China and Post-doctor Station of Management Science and Engineering, Nanchang University, Jiangxi 330031, ChinaJia-yu MaoDepartment of Mathematics, Nanchang University, Nanchang, Jiangxi 330031, China In this paper, iterative algorithm for strong vector equilibrium problem (SVEP) is studied.
Firstly, an auxiliary problem for SVEP is introduced
and the relationships between the auxiliary problem and SVEP are discussed.
Then, based on the auxiliary problem, a general iterative algorithm for SVEP is proposed.
Moreover, analysis of convergence of this general iterative algorithm is investigated
under suitable conditions of cone-continuity and cone-convexity.
The main results obtained in this paper extend and develop the corresponding ones
of [A. N. Iusem, W. Sosa, Optimization, \(\bf 52\) (2003), 301--316], [S.-H. Wang, Q.-Y. Li,
Optimization, \(\bf 64\) (2015), 2049--2063], and [B. Cheng, S.-Y. Liu,
J. Lanzhou Univ. Nat. Sci., \(\bf 45\) (2009), 105--109].
http://isr-publications.com/jnsa/5343/download-a-general-iterative-algorithm-for-vector-equilibrium-problemInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-190110820170824Existence of nonoscillatory solutions to nonlinear third-order neutral dynamic equations on time scales43524363http://dx.doi.org/10.22436/jnsa.010.08.28ENYang-Cong QiuSchool of Humanities and Social Science, Shunde Polytechnic, Foshan, Guangdong 528333, P. R. ChinaAkbar ZadaDepartment of Mathematics, University of Peshawar, Peshawar 25000, PakistanShuhong TangSchool of Information and Control Engineering, Weifang University, Weifang, Shandong 261061, P. R. ChinaTongxing LiSchool of Information Science and Engineering, Linyi University, Linyi, Shandong 276005, P. R. China and School of Control Science and Engineering, Shandong University, Jinan, Shandong 250061, P. R. China We study the existence of nonoscillatory solutions to a class of
third-order neutral functional dynamic equations on time scales. The
integral convergence and divergence of the reciprocal of the
coefficients in the equations are different. Two examples are given
to demonstrate the results.
http://isr-publications.com/jnsa/5344/download-existence-of-nonoscillatory-solutions-to-nonlinear-third-order-neutral-dynamic-equations-on-time-scalesInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-190110820170824The threshold of stochastic chemostat model with Monod-Haldane response function43644371http://dx.doi.org/10.22436/jnsa.010.08.29ENZhongwei CaoDepartment of Applied Mathematics, Jilin University of Finance and Economics, Changchun 130117, P. R. ChinaLiya LiuCollege of Science, China University of Petroleum, Qingdao 266580, Shandong Province, P. R. China This paper deals with problem of a stochastic chemostat model with Monod-Haldane response function. Firstly, we confirm the truth of the existence and uniqueness of the positive solution to the system. Then, we show the condition for the microorganism to be extinct. Moreover, we investigate there is a stationary distribution of this stochastic system and finally, we derive the expression for its invariant density.
http://isr-publications.com/jnsa/5345/download-the-threshold-of-stochastic-chemostat-model-with-monod-haldane-response-functionInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-190110820170824General \(L_p\)-mixed width-integral of convex bodies and related inequalities43724380http://dx.doi.org/10.22436/jnsa.010.08.30ENYanping ZhouDepartment of Mathematics, Shanghai University, Shanghai 200444, China The conception of general \(L_p\)-mixed width-integral of convex bodies is introduced and related isoperimetric type inequality, Aleksandrov-Fenchel type inequality and a cyclic inequality are established. Further, the extremum values for the general \(L_p\)-mixed width-integral are obtained.
http://isr-publications.com/jnsa/5346/download-general-l-p-mixed-width-integral-of-convex-bodies-and-related-inequalitiesInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-190110820170825Multiple periodic solutions for two classes of nonlinear difference systems involving classical \((\phi_1,\phi_2)\)-Laplacian43814397http://dx.doi.org/10.22436/jnsa.010.08.31ENXingyong ZhangDepartment of Mathematics, Faculty of Science, Kunming University of Science and Technology, Kunming, Yunnan 650500, P. R. ChinaLiben WangDepartment of Mathematics, Faculty of Science, Kunming University of Science and Technology, Kunming, Yunnan 650500, P. R. China In this paper, we investigate the
existence of multiple periodic solutions for two classes of nonlinear difference systems involving
\((\phi_1,\phi_2)\)-Laplacian. First, by using an important critical point theorem due to B. Ricceri, we establish an existence theorem of three periodic solutions for
the first nonlinear difference system with \((\phi_1,\phi_2)\)-Laplacian and two parameters. Moreover, for the second nonlinear difference
system with \((\phi_1,\phi_2)\)-Laplacian, by using the Clark's Theorem, we obtain a
multiplicity result of periodic solutions under a symmetric
condition. Finally, two examples are given to verify
our theorems.
http://isr-publications.com/jnsa/5357/download-multiple-periodic-solutions-for-two-classes-of-nonlinear-difference-systems-involving-classical-phi-1phi-2-laplacianInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-190110820170825A class of fractional order systems with not instantaneous impulses43984407http://dx.doi.org/10.22436/jnsa.010.08.32ENXianmin ZhangSchool of Mathematics and statistics, Yangtze Normal University, Fuling, Chongqing 408100, ChinaThis paper is concerned with a kind of fractional order systems with Caputo-Hadamard derivative (of order \(q\in\mathbb{C}\) and \(\Re(q)\in(1,2)\)) and not instantaneous impulses. The obtained result uncovers that there exists a general solution for these impulsive systems, which means that the state trajectory of these impulsive systems is non-unique, and it is expounded by a numerical example.
http://isr-publications.com/jnsa/5358/download-a-class-of-fractional-order-systems-with-not-instantaneous-impulsesInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-190110820170825Solutions of nonlinear systems by reproducing kernel method44084417http://dx.doi.org/10.22436/jnsa.010.08.33ENAliAkgülDepartment of Mathematics, Art and Science Faculty, Siirt University, 56100 Siirt, TurkeyYasir KhanDepartment of Mathematics, University of Hafr Al-Batin, Hafr Al-Batin 31991, Saudi ArabiaEsra Karatas AkgülGelibolu Piri Reis Vocational School, Canakkale Onsekiz Mart University, 17100, Canakkale, TurkeyDumitru BaleanuDepartment of Mathematics and Computer Sciences, Art and Science Faculty, Cankaya University, TR-06300 Ankara, TurkeyMaysaa Mohamed Al QurashiDepartment of Mathematics, King Saud University, Riyadh 12364, Saudi Arabia A novel approximate solution is obtained for viscoelastic fluid model by reproducing kernel method (RKM). The resulting equation for viscoelastic fluid with magneto-hydrodynamic flow is transformed to the nonlinear system by introducing the dimensionless variables. Results are presented graphically to study the efficiency and accuracy of the reproducing kernel method. Results show that this method namely RKM is an efficient method for solving nonlinear system in any engineering field.
http://isr-publications.com/jnsa/5360/download-solutions-of-nonlinear-systems-by-reproducing-kernel-methodInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-190110820170827Smooth solutions for the $p$-order functional equation \(f(\varphi(x))=\varphi^p(f(x))\)44184429http://dx.doi.org/10.22436/jnsa.010.08.34ENMin ZhangCollege of Science, China University of Petroleum, Qingdao, Shandong 266580, P. R. ChinaJie RuiCollege of Science, China University of Petroleum, Qingdao, Shandong 266580, P. R. China This paper deals with the \(p\)-order functional equation
\[\left\{
\begin{array}{ll}
f(\varphi(x))=\varphi^p(f(x)),\\
\varphi(0)=1, \quad -1\leq \varphi(x)\leq1 ,&\quad x\in[-1,1],
\end{array}
\right.
\]
where \(p\geq 2\) is an integer, \(\varphi^p\) is the \(p\)-fold iteration of
\(\varphi\), and \(f(x)\) is smooth odd function on
\([-1,1]\) and satisfies \(f(0)=0, -1<f^{'}(x)<0, (x\in[-1,1]).\)
Using constructive method, the existence of
unimodal-even-smooth solutions of the above equation on \([-1,1]\) can be proved.
http://isr-publications.com/jnsa/5380/download-smooth-solutions-for-the-p-order-functional-equation-fvarphixvarphipfxInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-190110820170827Positive solutions for a system of nonlinear semipositone fractional \(q\)-difference equations with \(q\)-integral boundary conditions44304440http://dx.doi.org/10.22436/jnsa.010.08.35ENWei ChengSchool of Mathematical Sciences, Chongqing Normal University, Chongqing 401331, ChinaJiafa XuSchool of Mathematical Sciences, Chongqing Normal University, Chongqing 401331, ChinaYujun CuiState Key Laboratory of Mining Disaster Prevention and Control Co-founded by Shandong Province, China In this paper, by virtue of fixed point index on cones, we obtain
two existence theorems of positive solutions for a system of
nonlinear semipositone fractional \(q\)-difference equations with
\(q\)-integral boundary conditions. Concave functions and nonnegative matrices are used to characterize the
coupling behavior of our nonlinearities.
http://isr-publications.com/jnsa/5381/download-positive-solutions-for-a-system-of-nonlinear-semipositone-fractional-q-difference-equations-with-q-integral-boundary-conditionsInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-190110820170827Extinction in a nonautonomous system of Volterra integrodifferential equations44414450http://dx.doi.org/10.22436/jnsa.010.08.36ENMeng HuSchool of mathematics and statistics, Anyang Normal University, Anyang Henan, 455000, ChinaLili WangSchool of mathematics and statistics, Anyang Normal University, Anyang Henan, 455000, China A nonautonomous system of Volterra integrodifferential equations is studied in this paper. It is
shown that if the coefficients are continuous, bounded above and below by positive constants
and satisfy certain inequalities, then one of the components will be driven to extinction while
the other one will stabilize at the certain positive solution of a nonlinear single species model.
http://isr-publications.com/jnsa/5382/download-extinction-in-a-nonautonomous-system-of-volterra-integrodifferential-equationsInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-190110820170827Singular left-definite Hamiltonian systems in the Sobolev space44514458http://dx.doi.org/10.22436/jnsa.010.08.37ENEkin UgurluDepartment of Mathematics, Faculty of Arts and Sciences, Cankaya University, 06530 Ankara, TurkeyKenan TasDepartment of Mathematics, Faculty of Arts and Sciences, Cankaya University, 06530 Ankara, TurkeyDumitru BaleanuDepartment of Mathematics, Faculty of Arts and Sciences, Cankaya University, 06530 Ankara, TurkeyThis paper is devoted to construct Weyl's theory for the singular
left-definite even-order Hamiltonian systems in the corresponding
Sobolev space. In particular, it is proved that there exist at least
\(n\)-linearly independent solutions in the Sobolev space for the
\(2n\)-dimensional Hamiltonian system.
http://isr-publications.com/jnsa/5383/download-singular-left-definite-hamiltonian-systems-in-the-sobolev-spaceInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-190110820170829A simultaneous Bregman projection methods for solving mixed split equality problems and fixed point problems in \(p\)-uniformly convex and uniformly smooth Banach spaces44594473http://dx.doi.org/10.22436/jnsa.010.08.38ENHaitao CheSchool of Mathematics and Information Science, Weifang University, Weifang, 261061, ChinaMeixia LiSchool of Mathematics and Information Science, Weifang University, Weifang, 261061, ChinaJingJing TanSchool of Mathematics and Information Science, Weifang University, Weifang, 261061, China In this article, a simultaneous Bregman projection scheme is introduced to approximate a common element of the set of fixed points of left Bregman strongly nonexpansive mapping and the set of solutions of mixed split equality problems in \(p (p\geq 2)\)-uniformly convex and uniformly smooth Banach spaces. We obtain the weak convergence theorem of the sequences generated by our scheme under some appropriate conditions. Furthermore, we apply our iterative algorithms to the split feasibility problem.
Finally, several numerical results are shown
to confirm the feasibility of the proposed methods. Our result presented in the article
are new and improve and extend some recent corresponding results.
http://isr-publications.com/jnsa/5398/download-a-simultaneous-bregman-projection-methods-for-solving-mixed-split-equality-problems-and-fixed-point-problems-in-p-uniformly-convex-and-uniformly-smooth-banach-spacesInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-190110820170829A numerical investigation on the structure of the zeros of the degenerate Euler-tangent mixed-type polynomials44744484http://dx.doi.org/10.22436/jnsa.010.08.39ENCheon Seoung RyooDepartment of Mathematics, Hannam University, Daejeon 306-791, Korea In this paper, we obtain a general symmetric identity involving the degenerate Euler-tangent mixed-type polynomials and sums of generalized falling factorials.
We use this identity to describe some combinatorial relations between these polynomials and generalized factorial alternating sums.
Finally, we observe an interesting phenomenon of "scattering" of the zeros
of degenerate Euler-tangent mixed-type polynomials.
http://isr-publications.com/jnsa/5399/download-a-numerical-investigation-on-the-structure-of-the-zeros-of-the-degenerate-euler-tangent-mixed-type-polynomialsInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-190110820170829Simpson-like type inequalities for relative semi-\((\alpha,m)\)-logarithmically convex functions44854498http://dx.doi.org/10.22436/jnsa.010.08.40ENChang ZhouDepartment of Mathematics, College of Science, China Three Gorges University, Yichang 443002, Hubei, P. R. ChinaCheng PengDepartment of Mathematics, College of Science, China Three Gorges University, Yichang 443002, Hubei, P. R. ChinaTingsong DuDepartment of Mathematics, College of Science, China Three Gorges University, Yichang 443002, Hubei, P. R. ChinaIn this paper, we derive a new integral identity concerning differentiable mappings defined on relative convex set. By using the obtained identity as an auxiliary result, we prove some new Simpson-like type inequalities for mappings whose absolute values of the first derivatives are relative semi-\((\alpha,m)\)-logarithmically convex. Several special cases are also discussed.
http://isr-publications.com/jnsa/5400/download-simpson-like-type-inequalities-for-relative-semi-alpham-logarithmically-convex-functionsInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-190110820170829Mazur-Ulam type theorems for fuzzy normed spaces44994506http://dx.doi.org/10.22436/jnsa.010.08.41ENJ. J. FontDepartament de Matemàtiques, and Institut Universitari de Matemàtiques i Aplicacions de Castelló (IMAC), Universitat Jaume I, Campus del Riu Sec. s/n, 12071 Castelló, SpainJ. GalindoDepartament de Matemàtiques, and Institut Universitari de Matemàtiques i Aplicacions de Castelló (IMAC), Universitat Jaume I, Campus del Riu Sec. s/n, 12071 Castelló, SpainS. MacarioDepartament de Matemàtiques, and Institut Universitari de Matemàtiques i Aplicacions de Castelló (IMAC), Universitat Jaume I, Campus del Riu Sec. s/n, 12071 Castelló, SpainM. SanchisDepartament de Matemàtiques, and Institut Universitari de Matemàtiques i Aplicacions de Castelló (IMAC), Universitat Jaume I, Campus del Riu Sec. s/n, 12071 Castelló, Spain In this paper, we provide Mazur-Ulam type results for (not necessarily surjective) maps preserving equality of fuzzy distance defined between two fuzzy normed spaces.
Our main goal is to study the additivity of such generalizations of fuzzy isometries.
As in the classical case, the fuzzy strict convexity of the target space will play an important role.
http://isr-publications.com/jnsa/5401/download-mazur-ulam-type-theorems-for-fuzzy-normed-spacesInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-190110820170829Approximation properties of solutions of a mean value type functional inequalities45074514http://dx.doi.org/10.22436/jnsa.010.08.42ENGinkyu ChoiDepartment of Electronic and Electrical Engineering, College of Science and Technology, Hongik University, 30016 Sejong, Republic of KoreaSoon-Mo JungMathematics Section, College of Science and Technology, Hongik University, 30016 Sejong, Republic of KoreaYang-Hi LeeDepartment of Mathematics Education, Gongju National University of Education, Gongju 32553, Republic of Korea We will prove the generalized Hyers-Ulam stability theorems of
a mean value type functional equation, namely
\[f(x) - g(y) = (x-y) h(sx + sy),\] which arises from the mean
value theorem.
As an application of our results, we introduce a
characterization of quadratic polynomials.
http://isr-publications.com/jnsa/5402/download-approximation-properties-of-solutions-of-a-mean-value-type-functional-inequalitiesInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-190110820170829A new Mittag-Leffler function undetermined coefficient method and its applications to fractional homogeneous partial differential equations45154523http://dx.doi.org/10.22436/jnsa.010.08.43ENYanQin LiuInstitute of Soft Matter Mechanics, Department of Engineering Mechanics, Hohai University, Jiangsu 210098, China and School of Mathematical Sciences, Dezhou University, Dezhou 253023, ChinaHongGuang SunInstitute of Soft Matter Mechanics, Department of Engineering Mechanics, Hohai University, Jiangsu 210098, ChinaXiuLing YinSchool of Mathematical Sciences, Dezhou University, Dezhou 253023, ChinaBaoGui XinNonlinear Science Center, College of Economics and Management, Shandong University of Science and Technology, Qingdao 266590, China In this paper, we develop a new application of the Mittag-Leffler function that will extend the application to fractional homogeneous differential equations, and propose a Mittag-Leffler function undetermined coefficient method. A new solution is constructed in power series. When a very simple ordinary differential equation is satisfied, no matter the original equation is linear or nonlinear, the method is valid, then combine the alike terms, compare the coefficient with identical powers, and the undetermined coefficient will be obtained. The fractional derivatives are described in the Caputo sense. To illustrate the reliability of the method, some examples are provided, and the solutions are in the form of generalized Mittag-Leffler function. The results reveal that the approach introduced here are very effective and convenient for solving homogeneous differential equations with fractional order.
http://isr-publications.com/jnsa/5403/download-a-new-mittag-leffler-function-undetermined-coefficient-method-and-its-applications-to-fractional-homogeneous-partial-differential-equationsInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-190110820170831Spectral analysis of quantum Dirac systems45244531http://dx.doi.org/10.22436/jnsa.010.08.44ENNihal YokusDepartment of Mathematics, Karamanoglu Mehmetbey University, 70100 Karaman, TurkeyNimet CoskunDepartment of Mathematics, Karamanoglu Mehmetbey University, 70100 Karaman, Turkey In this study, we establish the quantum calculus analogue of the classical
Dirac system. Moreover, we investigate the Jost solution, eigenvalues,
spectral singularities and some quantitative properties of the spectrum of
this new system.
http://isr-publications.com/jnsa/5413/download-spectral-analysis-of-quantum-dirac-systemsInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-190110820170831A class of differential inverse quasi-variational inequalities in finite dimensional spaces45324543http://dx.doi.org/10.22436/jnsa.010.08.45ENWei LiGeomathematics Key Laboratory of Sichuan Province, Chengdu University of Technology, Chengdu, Sichuan, 610059, P. R. ChinaYi-Bin XiaoSchool of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu, Sichuan, 611731, P. R. ChinaNan-Jing HuangDepartment of Mathematics, Sichuan University, Chengdu, 610064, P. R. ChinaYeol Je ChoDepartment of Mathematics Education and the RINS, Gyeongsang National University, Jinju 660-701, Korea In this paper, we introduce and study a class of differential inverse quasi-variational inequalities in finite dimensional Euclidean spaces, which are closely related to the differential variational inequalities. By using two important theorems on differential inclusions, we first prove some existence theorems for Carathéodory weak solutions of the differential inverse quasi-variational inequality considered. Then, with the Euler computation method, we construct an Euler time-dependent scheme for solving the differential inverse quasi-variational inequality and prove a convergence result on the Euler time-dependent scheme constructed.
http://isr-publications.com/jnsa/5414/download-a-class-of-differential-inverse-quasi-variational-inequalities-in-finite-dimensional-spacesInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-190110820170831Stability analysis for a class of nonlinear impulsive switched systems45444551http://dx.doi.org/10.22436/jnsa.010.08.46ENYuming FengKey Laboratory of Intelligent Information Processing and Control, School of Computer Science and Engineering, Chongqing Three\\ ~Gorges University, Wanzhou, Chongqing, 404100, P. R. ChinaLimin ZouSchool of Mathematics and Statistics, Chongqing Three Gorges University, Wanzhou, Chongqing, 404100, P. R. ChinaZhengwen TuSchool of Mathematics and Statistics, Chongqing Three Gorges University, Wanzhou, Chongqing, 404100, P. R. China
In this note, we show a new sufficient condition for exponentially stability for a class of nonlinear impulsive switched systems. Based on the result obtained, an effective computational method is devised for the construction of switched linear stabilizing feedback controllers. Finally, a numerical example is given to illustrate the feasibility of the proposed methods. Compared with the results shown by Xu and Teo [H.-L. Xu, K. L. Teo, IEEE Trans. Automat. Control, \({\bf 55}\) (2010), 2429--2433], the form of our result is simpler and its computational cost is lower. http://isr-publications.com/jnsa/5415/download-stability-analysis-for-a-class-of-nonlinear-impulsive-switched-systems