International Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-1901101020171012Homeomorphism metric space and the fixed point theorems51325141http://dx.doi.org/10.22436/jnsa.010.10.01ENYinglin LuoDepartment of Mathematics, Tianjin Polytechnic University, Tianjin 300387, ChinaYongfu SuDepartment of Mathematics, Tianjin Polytechnic University, Tianjin 300387, ChinaWenbiao GaoDepartment of Mathematics, Tianjin Polytechnic University, Tianjin 300387, China The purpose of this
paper is to introduce the concept of the homeomorphism metric
space and to prove the fixed point theorems and the best proximity
point theorems for generalized contractions in such spaces. The
multiplicative metric space is a special form of the homeomorphism
metric space. The results of this paper improve and extend the previously
known ones in the literature.http://isr-publications.com/jnsa/5775/download-homeomorphism-metric-space-and-the-fixed-point-theoremsInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-1901101020171012Degenerate ordered Bell numbers and polynomials associated with umbral calculus51425155http://dx.doi.org/10.22436/jnsa.010.10.02ENTaekyun KimDepartment of Mathematics, College of Science Tianjin Polytechnic University, Tianjin 300160, ChinaDae San KimDepartment of Mathematics, Sogang University, Seoul 121-742, Republic of KoreaGwan-Woo JangDepartment of Mathematics, Kwangwoon University, Seoul 139-701, Republic of KoreaLee-Chae JangGraduate School of Education, Konkuk University, Seoul 143-701, Republic of Korea In this paper, we study degenerate ordered Bell polynomials with the viewpoint of Carlitz's degenerate Bernoulli and Euler polynomials and derive by using umbral calculus some properties and new identities for the degenerate ordered Bell polynomials associated with special polynomials. http://isr-publications.com/jnsa/5776/download-degenerate-ordered-bell-numbers-and-polynomials-associated-with-umbral-calculusInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-1901101020171012Uniqueness and properties of positive solutions for infinite-point fractional differential equation with p-Laplacian and a parameter51565164http://dx.doi.org/10.22436/jnsa.010.10.03ENLi WangSchool of Mathematical Sciences, Shanxi University, Taiyuan 030006, Shanxi, P. R. ChinaChengbo ZhaiSchool of Mathematical Sciences, Shanxi University, Taiyuan 030006, Shanxi, P. R. China Using new methods for dealing with an infinite-point fractional differential equation with p-Laplacian and a parameter, we study the existence of unique positive solution for any given positive parameter \(\lambda\), and then give some clear properties of positive solutions which depend on the parameter \(\lambda>0\), that is, the positive solution \(u_\lambda^{*}\) is continuous, strictly increasing in \(\lambda\) and \(\lim_{\lambda\rightarrow +\infty}\|u_\lambda^*\|=+\infty,\lim_{\lambda\rightarrow 0^+}\|u_\lambda^*\|=0.\) Our analysis relies on some new theorems for operator equations \(A(x,x)=x\) and \(A(x,x)=\lambda x\), where \(A\) is a mixed monotone operator. http://isr-publications.com/jnsa/5777/download-uniqueness-and-properties-of-positive-solutions-for-infinite-point-fractional-differential-equation-with-p-laplacian-and-a-parameterInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-1901101020171012Convergence theorems and stability results of pointwise asymptotically nonexpansive mapping in Banach space51655173http://dx.doi.org/10.22436/jnsa.010.10.04ENQiansheng FengDepartment of Mathematics, Tianjin University, Tianjin, 300354, ChinaNan JiangDepartment of Mathematics, Tianjin University, Tianjin, 300354, ChinaYongfu SuDepartment of Mathematics, Tianjin Polytechnic University, Tianjin, 300387, China The purpose of this paper is to approximate
the fixed point of pointwise asymptotically nonexpansive mapping
using the generalized Mann and generalized Ishikawa iterative scheme.
And under the condition that the pointwise asymptotically nonexpansive
mapping is compact, the stability results of the two iterative schemes
are studied.
The main results of this paper modify and improve many important recent
results in the literature.
http://isr-publications.com/jnsa/5778/download-convergence-theorems-and-stability-results-of-pointwise-asymptotically-nonexpansive-mapping-in-banach-spaceInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-1901101020171012Estimates of higher order fractional derivatives at extreme points51745181http://dx.doi.org/10.22436/jnsa.010.10.05ENMohammed Al-RefaiDepartment of Mathematical Sciences, United Arab Emirates University, P. O. Box 15551, Al Ain, UAEDumitru BaleanuDepartment of Mathematics and Computer Science, Cankaya University, 06530 Ankara, Turkey We extend the results concerning the fractional derivatives of a
function at its extreme points to fractional derivatives of
arbitrary order. We also give an estimate of the error and present two examples to illustrate the validity of the results.
The presented results are valid for both Caputo and Riemann-Liouville fractional derivatives.
http://isr-publications.com/jnsa/5782/download-estimates-of-higher-order-fractional-derivatives-at-extreme-pointsInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-1901101020171012Nonlinear Mittag-Leffler stability of nonlinear fractional partial differential equations51825200http://dx.doi.org/10.22436/jnsa.010.10.06ENIbtisam Kamil HananInstitute of Engineering Mathematics, Universiti Malaysia Perlis, Pauh Putra Main Campus, 02600 Arau, Perlis, MalaysiaMuhammad Zaini AhmadInstitute of Engineering Mathematics, Universiti Malaysia Perlis, Pauh Putra Main Campus, 02600 Arau, Perlis, MalaysiaFadhel Subhi FadhelDepartment of Mathematics and Computer Applications, College of Science, Al-Nahrain University, P. O. Box 47077, Baghdad, Iraq This paper focuses on the application of fractional backstepping control scheme for nonlinear fractional partial differential equation (FPDE). Two types of fractional derivatives are considered in this paper, Caputo and the Grünwald-Letnikov fractional derivatives. Therefore, obtaining highly accurate approximations for this derivative is of a great
importance. Here, the discretized approach for the space variable is used to transform the FPDE into a system of fractional differential equations. The convergence of the closed loop system is guaranteed in the sense of Mittag-Leffler stability. An illustrative example is given to demonstrate the effectiveness of the proposed control scheme.
http://isr-publications.com/jnsa/5784/download-nonlinear-mittag-leffler-stability-of-nonlinear-fractional-partial-differential-equationsInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-1901101020171014Impact of non-separable incidence rates on global dynamics of virus model with cell-mediated, humoral immune responses52015218http://dx.doi.org/10.22436/jnsa.010.10.07ENYoichi EnatsuDepartment of Applied Mathematics, Tokyo University of Science, 1-3 Kagurazaka, Shinjuku-ku, Tokyo 162-8601, JapanJinliang WangSchool of Mathematical Science, Heilongjiang University, Harbin 150080, ChinaToshikazu KuniyaGraduate School of System Informatics, Kobe University, 1-1 Rokkodai-cho, Nada-ku, Kobe 657-8501, Japan
In this paper, we study the dynamical behavior of a virus model into which cell-mediated and humoral immune responses are incorporated. The global stability of an infection-free equilibrium and four infected equilibria is established via a Lyapunov functional approach. The present construction methods are applicable to a wide range of incidence rates that are monotone increasing with respect to concentration of uninfected cells and concave with respect to the concentration of free virus particles. In addition, when the incidence rate is monotone increasing with respect to concentration of free virus particles, the functional approach plays an important role in determining the global stability of each of the four infected equilibria. This implies that the dynamical behavior of virus prevalence would be determined by basic reproduction numbers when the ``saturation effect" for free virus particles appears. We point out that the incidence rate includes not only separable incidence rate but also non-separable incidence rate such as standard incidence and Beddington-DeAngelis functional response.http://isr-publications.com/jnsa/5794/download-impact-of-non-separable-incidence-rates-on-global-dynamics-of-virus-model-with-cell-mediated-humoral-immune-responsesInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-1901101020171014Existence of solution and Hyers-Ulam stability for a coupled system of fractional differential equations with \(p\)-Laplacian operator52195229http://dx.doi.org/10.22436/jnsa.010.10.08ENHasib KhanState Key Laboratory of Hydrology-Water Resources and Hydraulic Engineering, Hohai University, 210098, Nanjing, P. R. ChinaYongjin LiDepartment of Mathematics, Sun Yat-sen University, 510275, Guangzhou, P. R. ChinaHongguang SunState Key Laboratory of Hydrology-Water Resources and Hydraulic Engineering, Hohai University, 210098, Nanjing, P. R. ChinaAziz KhanDepartment of Mathematics, University of Peshawar, 25000, Khyber Pakhtunkhwa, Pakistan
Models with \(p\)-Laplacian operator are common in different scientific fields including; plasma physics, chemical reactions design, physics, biophysics, and many others. In this paper, we investigate existence and uniqueness of solution and Hyers-Ulam stability for a coupled system of fractional differential equations with \(p\)-Laplacian operator. The Hyers-Ulam stability means that a differential equation
has a close exact solution which is generated by the approximate solution of the differential equation and the error in the approximation can be estimated. We use topological degree method and provide an expressive example as an application of the work. http://isr-publications.com/jnsa/5795/download-existence-of-solution-and-hyers-ulam-stability-for-a-coupled-system-of-fractional-differential-equations-with-p-laplacian-operatorInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-1901101020171019Reduced differential transform method for solving time and space local fractional partial differential equations52305238http://dx.doi.org/10.22436/jnsa.010.10.09ENOmer AcanDepartment of Mathematics, Art and Science Faculty, Siirt University, Siirt, TurkeyMaysaa’ Mohamed Al QurashiDepartment of Mathematics, Faculty of Art and Science, King Saud University, P. O. Box 22452, Riyadh 11495, Saudi ArabiaDumitru BaleanuDepartment of Mathematics and Computer Sciences, Faculty of Art and Science, Cankaya University, Ankara, Turkey
We apply the new local fractional reduced differential transform method to obtain the solutions of some linear and nonlinear partial differential equations on Cantor set. The reported results are compared with the related solutions presented in the literature and the graphs are plotted to show their behaviors. The results prove that the presented method is faster and easy to apply.http://isr-publications.com/jnsa/5848/download-reduced-differential-transform-method-for-solving-time-and-space-local-fractional-partial-differential-equationsInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-1901101020171019Sensitivity of non-autonomous discrete dynamical systems revisited52395244http://dx.doi.org/10.22436/jnsa.010.10.10ENXian-Feng DingSchool of Sciences, Southwest Petroleum University, Chengdu, Sichuan, 610500, PeopleTian-Xiu LuSchool of Mathematics and Statistics, Sichuan University of Science and Engineering, Zigong, Sichuan, 643000, PeopleJian-Jun WangDepartment of Applied Mathematics, Sichuan Agricultural University, Ya In this note, we construct a transitive non-autonomous discrete
system with strongly periodic density which is not sensitive.
Besides, we prove that every transitive non-autonomous discrete
system with almost periodic density is syndetically sensitive,
provided that it converges uniformly to a map, and that a product
system is multi-sensitive (resp., \(\mathcal{F}\)-sensitive) if and only
if there exists a factor system is multi-sensitive (resp., \(\mathcal{F}\)-sensitive),
where \(\mathcal{F}\) is a filterdual.
http://isr-publications.com/jnsa/5849/download-sensitivity-of-non-autonomous-discrete-dynamical-systems-revisitedInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-1901101020171019Two-step Maruyama schemes for nonlinear stochastic differential delay equations52455260http://dx.doi.org/10.22436/jnsa.010.10.11ENDongxia LeiSchool of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan, 430074, ChinaXiaofeng ZongSchool of Automation, China University of Geosciences, Wuhan, 430074, ChinaJunhao HuSchool of Mathematics and Statistics, South-Central University for Nationalities, Wuhan, 430074, China This work concerns the two-step Maruyama schemes for nonlinear stochastic differential delay equations (SDDEs). We first examine the strong convergence rates of the split two-step Maruyama scheme and linear two-step Maruyama scheme (including Adams-Bashforth and Adams-Moulton schemes) for nonlinear SDDEs with highly nonlinear delay variables, then we investigate the exponential mean square stability and exponential decay rates of the two classes of two-step Maruyama schemes. These results are important for three reasons: first, the convergence rates are established under the non-global Lipschitz condition; second, these stability results show that these two-step Maruyama schemes can not only reproduce the exponential mean square stability, but also preserve the bound of Lyapunov exponent for sufficient small stepsize; third, they are also suitable for the corresponding two-step Maruyama methods of stochastic ordinary differential equations (SODEs).
http://isr-publications.com/jnsa/5850/download-two-step-maruyama-schemes-for-nonlinear-stochastic-differential-delay-equationsInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-1901101020171019Common fixed points of generalized rational contractions on a closed ball in partial metric spaces52615270http://dx.doi.org/10.22436/jnsa.010.10.12ENMuhammad NazamDepartment of Mathematics, International Islamic University Islamabad, PakistanMuhammad ArshadDepartment of Mathematics and Statistics, International Islamic University, H-10, Islamabad, PakistanChoonkil ParkResearch Institute for Natural Sciences, Hanyang University, Seoul 04763, Republic of KoreaSungsik YunDepartment of Financial Mathematics, Hanshin University, Gyeonggi-do 18101, Republic of Korea
The notion of generalized contractions of rational type on a closed ball is introduced and used to establish some common fixed point theorems for two, three and four mappings in complete ordered partial metric spaces. These results improve several well-known, primary and conventional results. We give an example to illustrate the main idea of our results that there are mappings which have only fixed points inside or on the closed ball instead of whole space.http://isr-publications.com/jnsa/5851/download-common-fixed-points-of-generalized-rational-contractions-on-a-closed-ball-in-partial-metric-spacesInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-1901101020171019Second-order differential superordination for analytic functions in the upper half-plane52715280http://dx.doi.org/10.22436/jnsa.010.10.13ENHuo TangSchool of Mathematics and Statistics, Chifeng University, Chifeng 024000, Inner Mongolia, People's Republic of ChinaH. M. SrivastavaDepartment of Mathematics and Statistics, University of Victoria, Victoria, British Columbia V8W 3R4, CanadaGuan-Tie DengSchool of Mathematical Sciences, Beijing Normal University, Beijing 100875, People's Republic of ChinaShu-Hai LiSchool of Mathematics and Statistics, Chifeng University, Chifeng 024000, Inner Mongolia, People's Republic of China
Let \(\Omega\) be a set in the complex plane \(\mathbb{C}\). Also let \(p(z)\) be analytic in the upper half-plane \(\Delta=\{z:z\in\mathbb{C}\ \text{and}\ \Im(z)>0\}\) and suppose that \(\psi: \mathbb{C}^3\times\Delta\rightarrow\mathbb{C}\).
In this paper, we investigate the problem of determining properties of functions \(p(z)\) that satisfy the following second-order differential superordination:
\[\Omega\subset\left\{\psi\left(p(z),p'(z),p''(z);z\right): z\in\Delta\right\}.\]
Applications of these results to second-order differential superordination for analytic functions in \(\Delta\) are also presented.http://isr-publications.com/jnsa/5852/download-second-order-differential-superordination-for-analytic-functions-in-the-upper-half-planeInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-1901101020171019Positive solution for a coupled system of nonlinear fractional differential equations with fractional integral conditions52815291http://dx.doi.org/10.22436/jnsa.010.10.14ENYaohong LiCenter of Statistical Survey and Advising, Suzhou University, 234000 Anhui , P. R. ChinaHaiyan ZhangSchool of Mathematics and Statistics, Suzhou University, 234000 Anhui , P. R. China By studying the properties of Green's function, constructing a
special cone and applying fixed point theorem of cone expansion and
compression of norm type, this paper investigates the existence of
at least one and two positive solutions for a coupled system of
nonlinear fractional differential equations involving fractional
integral conditions and derivatives of arbitrary order. Two examples
are given to illustrate our results.
http://isr-publications.com/jnsa/5855/download-positive-solution-for-a-coupled-system-of-nonlinear-fractional-differential-equations-with-fractional-integral-conditionsInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-1901101020171020Uniform convexity in \(\ell_{p(\cdot)}\)52925299http://dx.doi.org/10.22436/jnsa.010.10.15ENMostafa BacharDepartment of Mathematics, College of Sciences, King Saud University, Riyadh, Saudi ArabiaMessaoud BounkhelDepartment of Mathematics, College of Sciences, King Saud University, Riyadh, Saudi ArabiaMohamed A. KhamsiDepartment of Mathematical Sciences, University of Texas at El Paso, El Paso, TX 79968, USA In this work, we investigate the variable exponent sequence space \(\ell_{p(\cdot)}\). In particular, we prove a geometric property similar to uniform convexity without the assumption \(\limsup_{n \to \infty} p(n) < \infty\). This property allows us to prove the analogue to Kirk's fixed point theorem in the modular vector space \(\ell_{p(\cdot)}\) under Nakano's formulation.
http://isr-publications.com/jnsa/5856/download-uniform-convexity-in-ell-pcdotInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-1901101020171020Caustics of translation surfaces in Euclidean \(3\)-space53005310http://dx.doi.org/10.22436/jnsa.010.10.16ENJingren ChenSchool of Mathematical Sciences, Harbin Normal University, Harbin, 150025, P. R. ChinaHaiming LiuSchool of Mathematical Sciences, Mudanjiang Normal University, Mudanjiang, 157011, P. R. ChinaJiajing MiaoSchool of Mathematical Sciences, Mudanjiang Normal University, Mudanjiang, 157011, P. R. China The aim of this paper is to classify the singularities of caustics, which have implications for a wide range of physical applications, of translation
surfaces. In addition, we give a particular study on ridge point,
sub-parabolic ridge point, and constant curvature line on
translation surface and we find that there is no elliptic umblic
on translation surface.
http://isr-publications.com/jnsa/5857/download-caustics-of-translation-surfaces-in-euclidean-3-spaceInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-1901101020171020Application of penalty methods to generalized variational inequalities in Banach spaces53115320http://dx.doi.org/10.22436/jnsa.010.10.17ENG. W. SuGuangxi Key Laboratory Cultivation Base of Cross-border E-commerce Intelligent Information Processing, College of Information and Statistics, Guangxi University of Finance and Economics, Nanning, Guangxi, 530003, P. R. ChinaZ. W. ZhaoGuangxi Key Laboratory of Universities Optimization Control and Engineering Calculation, and College of Sciences, Guangxi University for Nationalities, Nanning, Guangxi 530006, P. R. China In this paper, we consider a class of generalized variational
inequalities (GVI) in infinite dimensional Banach spaces, in which
only approximation sequences for GVI are known instead of exact
values of the cost mapping and feasible set. A sequence of inexact
solutions of auxiliary problems involving general penalty method is
introduced. We obtain some convergence properties of the perturbed
version of the regularized penalty method under mild coercive
conditions, which extend some well-known results of variational
inequalities in many respects.
http://isr-publications.com/jnsa/5858/download-application-of-penalty-methods-to-generalized-variational-inequalities-in-banach-spacesInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-1901101020171020On monotone multivalued transformations53215327http://dx.doi.org/10.22436/jnsa.010.10.18ENButhinah A. Bin DehaishDepartment of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah, Saudi ArabiaMohamed A. KhamsiDepartment of Mathematics \(\&\) Statistics, King Fahd University of Petroleum and Minerals Dhahran 31261, Saudi Arabia and Department of Mathematical Sciences, University of Texas at El Paso, El Paso, TX 79968, U.S.A. In this work, we discuss the recently introduced monotone \(\tau\)-Opial condition in Banach spaces which admit a sequence of monotone approximations of the identity. Then we give a fixed point theorem for monotone multivalued nonexpansive mappings in Banach spaces satisfying the monotone \(\tau\)-Opial condition. This result generalizes those of Markin, Browder and Lami Dozo to monotone mappings.
http://isr-publications.com/jnsa/5859/download-on-monotone-multivalued-transformationsInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-1901101020171020Existence of solutions for fractional differential equations with integral boundary conditions at resonance53285341http://dx.doi.org/10.22436/jnsa.010.10.19ENWei ZhangDepartment of Mathematics, China University of Mining and Technology, Xuzhou 221116, P. R. ChinaWenbin LiuDepartment of Mathematics, China University of Mining and Technology, Xuzhou 221116, P. R. China This paper investigates the existence of solutions for Riemann-Stieltjes integral boundary value problems of fractional differential equation by using Mawhin's coincidence degree theory. An example is given to show the application of our result.
http://isr-publications.com/jnsa/5860/download-existence-of-solutions-for-fractional-differential-equations-with-integral-boundary-conditions-at-resonanceInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-1901101020171020Nonlinear contractions and fixed point theorems with modified $\omega$-distance mappings in complete quasi metric spaces53425350http://dx.doi.org/10.22436/jnsa.010.10.20ENInam NuseirDepartment of Mathematics and Statistics, Jordan University of Science and Technology, P. O. Box 3030, Irbid 22110, JordanWasfi ShatanawiDepartment of Mathematics and General Courses, Prince Sultan University, Riyadh, Saudi ArabiaIssam Abu-IrwaqDepartment of Mathematics and Statistics, Jordan University of Science and Technology, P. O. Box 3030, Irbid 22110, JordanAnwar BataihahDepartment of Mathematics, The University of Jordan, Amman, Jordan Alegre and Marin [C. Alegre, J. Marin, Topol. Appl., \({\bf 203}\) (2016), 32--41] introduced
the concept of modified \(\omega\)-distance mappings on a complete
quasi metric space in which they studied some fixed point results.
In this manuscript, we prove some fixed point results of nonlinear
contraction conditions through modified \(\omega\)-distance mapping on
a complete quasi metric space in sense of Alegre and Marin.
http://isr-publications.com/jnsa/5861/download-nonlinear-contractions-and-fixed-point-theorems-with-modified-omega-distance-mappings-in-complete-quasi-metric-spacesInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-1901101020171020Viscosity approximation of solutions of a split feasibility problem in Hilbert spaces53515359http://dx.doi.org/10.22436/jnsa.010.10.21ENYantao YangCollege of Mathematics and Computer Science, Yanan University, Yanan, ChinaYunpeng ZhangInst. Fundamental \(\&\) Frontier Sci., Univ. Elect. Sci. \(\&\) Technol. China, Chenghua District, Chengdu, China In this paper, we study two viscosity approximation iterative methods for solving solutions of a split feasibility problem. Strong convergence theorems are established in the framework of infinite dimensional Hilbert spaces.
http://isr-publications.com/jnsa/5862/download-viscosity-approximation-of-solutions-of-a-split-feasibility-problem-in-hilbert-spacesInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-1901101020171020Positive solutions to nonlinear fractional differential equations involving Stieltjes integrals conditions53605372http://dx.doi.org/10.22436/jnsa.010.10.22ENJiqiang JiangSchool of Mathematical Sciences, Qufu Normal University, Qufu 273165, Shandong, People's Republic of ChinaLishan LiuSchool of Mathematical Sciences, Qufu Normal University, Qufu 273165, Shandong, People's Republic of ChinaYonghong WuDepartment of Mathematics and Statistics, Curtin University, Perth, WA 6845, Australia In this paper, we consider the existence of positive solutions for a
class of nonlinear fractional semipositone differential equations
involving integral boundary conditions. Some existence results of
positive solutions are obtained by means of Leray-Schauder's
alternative and Krasnoselskii's fixed point theorem. An example is
given to demonstrate the application of our main results.
http://isr-publications.com/jnsa/5863/download-positive-solutions-to-nonlinear-fractional-differential-equations-involving-stieltjes-integrals-conditionsInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-1901101020171027Well-posedness for systems of generalized mixed quasivariational inclusion problems and optimization problems with constraints53735392http://dx.doi.org/10.22436/jnsa.010.10.23ENLu-Chuan CengDepartment of Mathematics, Shanghai Normal University, Shanghai 200234, ChinaYeong-Cheng LiouDepartment of Healthcare Administration and Medical Informatics, Center for Big Data Analytics \(\&\) Intelligent Healthcare, and Research Center of Nonlinear Analysis and Optimization, Kaohsiung Medical University, Kaohsiung 807, TaiwanJen-Chih YaoCenter for General Education, China Medical University, Taichung, 40402, TaiwanYonghong YaoDepartment of Mathematics, Tianjin Polytechnic University, Tianjin 300387, ChinaChing-Hua LoDepartment of Mathematics, Tianjin Polytechnic University, Tianjin 300387, China In this paper, several metric characterizations of well-posedness for
systems of generalized mixed quasivariational inclusion problems and for optimization problems with systems of generalized mixed quasivariational
inclusion problems as constraints are given. The equivalence between the well-posedness of systems of generalized mixed quasivariational inclusion
problems and the existence of solutions of systems of generalized mixed quasivariational inclusion problems is given under suitable conditions.
http://isr-publications.com/jnsa/5937/download-well-posedness-for-systems-of-generalized-mixed-quasivariational-inclusion-problems-and-optimization-problems-with-constraintsInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-1901101020171027An inverse nodal problem for \({p}\)-Laplacian Sturm-Liouville equation with Coulomb potential53935401http://dx.doi.org/10.22436/jnsa.010.10.24ENTuba GulsenDepartment of Mathematics, Firat University, 23119, Elazig, Turkey We deal with an inverse nodal problem for
\(p\)-Laplacian Sturm-Liouville equation which
includes Coulomb type potential function under boundary condition depends on
polynomial spectral parameter. Here, we get some asymptotic formulas of
eigenvalues and nodal parameters by using a suitable Prüfer substitution. Eventually, we construct Coulomb potential by using nodal
lengths.
http://isr-publications.com/jnsa/5938/download-an-inverse-nodal-problem-for-p-laplacian-sturm-liouville-equation-with-coulomb-potentialInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-1901101020171027The rapid convergence for nonlinear singular differential systems with "maxima''54025421http://dx.doi.org/10.22436/jnsa.010.10.25ENPeiguang WangCollege of Mathematics and Information Science, Hebei University, Baoding, Hebei 071002, ChinaXiang LiuCollege of Mathematics and Information Science, Hebei University, Baoding, Hebei 071002, ChinaTongxing LiSchool of Information Science and Engineering, Linyi University, Linyi, Shandong 276005, China This paper investigates the initial value problem for a class of nonlinear singular differential systems with "maxima''. By using the
comparison principle and the approximate quasilinearization method, we obtain two monotone iterative sequences of approximate solutions
which converge uniformly and rapidly to the solution of such systems.
http://isr-publications.com/jnsa/5939/download-the-rapid-convergence-for-nonlinear-singular-differential-systems-with-maximaInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-1901101020171027Modelling the movement of groundwater pollution with variable order derivative54225432http://dx.doi.org/10.22436/jnsa.010.10.26ENS. N. KameniAfrican Institute for Mathematical Sciences (AIMS), P. O. Box 608, Limbe Crystal Gardens, South West Region, CameroonJ. D. DjidaAfrican Institute for Mathematical Sciences (AIMS), P. O. Box 608, Limbe Crystal Gardens, South West Region, CameroonA. AtanganaInstitute for Groundwater Studies, Faculty of Natural and Agricultural Sciences, University of the Free State, 9301, Bloemfontein, South Africa In this paper, a new concept of variable differentiation is used to revisit the model of groundwater pollution. The new variable order derivation has a non-singular kernel and can be used for analytical and numerical purposes. The novel model is solved via Fourier transform method. We solve numerically the new equation using the implicit finite difference scheme and study the stability and convergence of that scheme.
http://isr-publications.com/jnsa/5940/download-modelling-the-movement-of-groundwater-pollution-with-variable-order-derivativeInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-1901101020171027Strong convergence theorems for the general split common fixed point problem in Hilbert spaces54335444http://dx.doi.org/10.22436/jnsa.010.10.27ENRudong ChenDepartment of Mathematics, Tian jin Polytechnic University, Tian jin 300387, ChinaTao SunDepartment of Mathematics, Tian jin Polytechnic University, Tian jin 300387, ChinaHuimin HeSchool of Mathematics and Statistics, Xidian University, Xi'an 710071, ChinaJen-Chih YaoCenter for General Education, China Medical University, Taichung 40402, Taiwan, ROC
In this paper, we propose and investigate a new iterative algorithm for solving the general split common fixed point problem in the setting of infinite-dimensional Hilbert spaces. We also prove the sequence generated by the proposed algorithm converge strongly to a common solution of the general split common fixed point problem. As application, some particular cases of directed operator and quasi-nonexpansive operator are also considered. Finally, we present several numerical results for general split common fixed point problem to demonstrate the efficiency of the proposed algorithm. http://isr-publications.com/jnsa/5941/download-strong-convergence-theorems-for-the-general-split-common-fixed-point-problem-in-hilbert-spacesInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-1901101020171028Existence, non-existence and multiplicity results for a third order eigenvalue three-point boundary value problem54455463http://dx.doi.org/10.22436/jnsa.010.10.28ENAlberto CabadaInstituto de Matemáticas, Facultade de Matemáticas, Universidade de Santiago de Compostela, 15782 Santiago de Compostela, Spain LucíaLópez-SomozaInstituto de Matemáticas, Facultade de Matemáticas, Universidade de Santiago de Compostela, 15782 Santiago de Compostela, SpainFelizMinhósDepartamento de Matemática, Escola de Ciências e Tecnologia, Centro de Investigação em Matemática e Aplicações (CIMA), Instituto de Investigação e Formação Avançada, Universidade de Évora. Rua Romão Ramalho, 59, 7000-671 Évora, Portugal
This paper provides sufficient conditions to guarantee the existence, non-existence and multiplicity of solutions for a third order eigenvalue fully differential equation, coupled with three point boundary value conditions.
Although the change of sign, some bounds for the second derivative of the Green's function are obtained, which allow to define a different kind of cone that, as far as we know, has not been previously used in the literature.
The main arguments are based on the fixed point index theory for bounded and unbounded sets. Some examples are presented in order to show that the different existence theorems proved are not comparable.http://isr-publications.com/jnsa/5942/download-existence-non-existence-and-multiplicity-results-for-a-third-order-eigenvalue-three-point-boundary-value-problemInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-1901101020171028New criteria on exponential synchronization and existence of periodic solutions of complex BAM networks with delays54645482http://dx.doi.org/10.22436/jnsa.010.10.29ENChao YangDepartment of Mathematics and Computer Science, Changsha University, Changsha 410022, P. R. ChinaLihong HuangSchool of Mathematical and Statistics, Changsha University of Science and Technology, Changsha, Hunan 410114, P. R. China In this paper, we study a class of time-delayed BAM neural networks with discontinuous activations. Base on the framework of differential inclusion theory and set-valued analysis, by designing discontinuous feedback controller and using some analytic methods, easily verifiable delay-independent criteria are established to guarantee the existence of periodic solution and global exponential synchronization of the drive-response system. Finally, we give a numerical example to illustrate our theoretical analysis. The obtained results are essentially new and they extend previously known results.
http://isr-publications.com/jnsa/5943/download-new-criteria-on-exponential-synchronization-and-existence-of-periodic-solutions-of-complex-bam-networks-with-delaysInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-1901101020171028Weak convergence of a modified subgradient extragradient algorithm for monotone variational inequalities in Banach spaces54835494http://dx.doi.org/10.22436/jnsa.010.10.30ENYing LiuCollege of Mathematics and Information Science, Hebei University, Baoding, Hebei, 071002, ChinaHang KongCollege of Mathematics and Information Science, Hebei University, Baoding, Hebei, 071002, China Applying the generalized projection operator, we introduce a modified subgradient extragradient algorithm in Banach spaces for a variational inequality involving a monotone Lipschitz continuous
mapping which is more general than an inverse-strongly-monotone mapping. Weak convergence of the iterative algorithm is also proved. An advantage of the algorithm is the computation of only one value of the inequality
mapping and one projection onto the admissible set per one iteration.
http://isr-publications.com/jnsa/5944/download-weak-convergence-of-a-modified-subgradient-extragradient-algorithm-for-monotone-variational-inequalities-in-banach-spacesInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-1901101020171031Existence of fixed points for \(\gamma\)-\(FG\)-contractive condition via cyclic \((\alpha,\beta)\)-admissible mappings in \(b\)-metric spaces54955508http://dx.doi.org/10.22436/jnsa.010.10.31ENSaroj Kumar PadhanDepartment of Mathematics, Veer Surendra Sai University of Technology, Burla, Sambalpur, Odisha-768018, INDIAG V V Jagannadha RaoDepartment of Mathematics, Veer Surendra Sai University of Technology, Burla, Sambalpur, Odisha-768018, INDIAAhmed Al-RawashdehDepartment of Mathematical sciences, UAE University, 1555, Al Ain, U.A.E.Hemant Kumar NashineDepartment of Mathematics, Texas A \(\&\) M University-Kingsville-78363-8202, Texas, U.S.A.Ravi P. AgarwalDepartment of Mathematics, Texas A \(\&\) M University-Kingsville-78363-8202, Texas, U.S.A.
In this paper, we introduce a new concept of cyclic \((\alpha,\beta)\)-type \(\gamma\)-\(FG\)-contractive mapping
and we prove some fixed point theorems for such mappings in complete \(b\)-metric spaces.
Suitable examples are introduced to verify the main results.
As an application, we obtain sufficient conditions for the existence of solutions for
nonlinear integral equation which are illustrated by an example. http://isr-publications.com/jnsa/5991/download-existence-of-fixed-points-for-gamma-fg-contractive-condition-via-cyclic-alphabeta-admissible-mappings-in-b-metric-spacesInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-1901101020171031Some fixed point results for \(\alpha\)-nonexpansive maps on partial metric spaces55095527http://dx.doi.org/10.22436/jnsa.010.10.32ENHassen AydiDepartment of Mathematics, College of Education of Jubail, Imam Abdulrahman Bin Faisal University, P. O.: 12020, Industrial Jubail, 31961, Saudi ArabiaAbdelbasset FelhiDepartment of Mathematics and Physics, Preparatory Engineering Institute, Bizerte, Carthage University, Tunisia
In this paper, we prove some fixed point results for a class of \(\alpha\)-nonexpansive single and multi-valued mappings in the setting of partial metric spaces.
Our results generalize the analogous ones of Vetro [F. Vetro, Filomat, \(\bf 29\) (2015), 2011--2020]. Some examples are presented making our results effective.
http://isr-publications.com/jnsa/5992/download-some-fixed-point-results-for-alpha-nonexpansive-maps-on-partial-metric-spacesInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-1901101020171031On nonlinear implicit fractional differential equations without compactness55285539http://dx.doi.org/10.22436/jnsa.010.10.33ENSamia BushnaqDepartment of Science, Princess Sumaya University for Technology, Amman 11941, JordanWajid HussainDepartment of Mathematics, University of Qurtuba, Peshawar, Khyber Pakhtunkhwa, PakistanKamal ShahDepartment of Mathematics, University of Malakand, Chakdara, Dir(L), Khyber Pakhtunkhwa, Pakistan
The main purpose of this research paper is to develop some sufficient
conditions for the existence of solution of a nonlinear problem of
implicit fractional differential equations (IFDEs) with boundary conditions, using
prior estimate method. The distinction of the method applied here
is, it does not require compactness of the operator. This idea is
the result of motivation from the book of O'Regan and other [R. P. Agarwal, D. O'Regan, Y. J. Cho, Y.-Q. Chen, Taylor \(\&\) Francis Group, New York, (2006)].
Devising the respective conditions, we also developed some conditions
for Hyers-Ulam type stability to the solution of the said problem.
To justify the relevant results a suitable example is provided.http://isr-publications.com/jnsa/5993/download-on-nonlinear-implicit-fractional-differential-equations-without-compactnessInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-1901101020171031Minimizing the object space error for pose estimation: towards the most efficient algorithm55405551http://dx.doi.org/10.22436/jnsa.010.10.34ENYingwei HanSchool of Economics and Management, Beihang University, Beijing, 100191, ChinaYong XiaSchool of Mathematics and System Sciences, Beihang University, 100191, ChinaPing LiSchool of Economics and Management, Beihang University, Beijing, 100191, China In this paper, we present an efficient branch-and-bound algorithm to
globally minimize the object space error for the camera pose
estimation. The key idea is to reformulate the pose estimation
model using the optimal Lagrangian multipliers.
Numerical simulation results show that our algorithm usually
terminates in the first iteration and finds an \(\epsilon\)-suboptimal
solution.
Furthermore, the efficiency of our algorithm is demonstrated by a comprehensive numerical
comparison with two well-known heuristics. We also demonstrate the computational
power of our algorithm by comparing it with the state-of-the-art
global optimization package BARON.
http://isr-publications.com/jnsa/5997/download-minimizing-the-object-space-error-for-pose-estimation-towards-the-most-efficient-algorithmInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-1901101020171031Stochastic shadowing analysis of a class of stochastic differential equations55525565http://dx.doi.org/10.22436/jnsa.010.10.35ENQingyi ZhanCollege of Computer and Information Science, Fujian Agriculture and Forestry University, Fuzhou, Fujian 350002, P. R. ChinaYuhong LiCollege of Hydropower and Information Engineering, Huazhong University of Science and Technology, Wuhan, 430074, P. R. China
This paper is devoted to the feasibility of stochastic shadowing of a class of stochastic differential equations via numerical analysis tools. A general shadowing theorem of stochastic differential equations is proven, and an explicit relationship of shadowing and the coefficients of SDE, a bound for shadowing distance are both investigated. The focus is explicit regularity conditions of stochastic differential equations which can ensure the shadowing.
A numerical experiment is provided to illustrate the effectiveness of the proposed theorem by the numerical simulations of chaotic orbits of the stochastic Lorenz equations. http://isr-publications.com/jnsa/5998/download-stochastic-shadowing-analysis-of-a-class-of-stochastic-differential-equationsInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-1901101020171031Perturbation resilience of proximal gradient algorithm for composite objectives55665575http://dx.doi.org/10.22436/jnsa.010.10.36ENYanni GuoCollege of Science, Civil Aviation University of China, Tianjin, 300300, P. R. ChinaWei CuiCollege of Science, Civil Aviation University of China, Tianjin, 300300, P. R. ChinaYansha GuoSchool of Information Technology Engineering, Tianjin University of Technology and Education, Tianjin, 300222, P. R. China In this paper, we study the perturbation resilience of a proximal gradient algorithm
under the general Hilbert space setting. With the assumption that the error sequence
is summable, we prove that the iterative sequence converges weakly to a solution of the composite
optimization problem. We also show the bounded perturbation resilience of this iterative
method and apply it to the lasso problem.
http://isr-publications.com/jnsa/5999/download-perturbation-resilience-of-proximal-gradient-algorithm-for-composite-objectivesInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-1901101020171031Existence of solutions to boundary value problems for a higher-dimensional difference system55765584http://dx.doi.org/10.22436/jnsa.010.10.37ENTao ZhouSchool of Business Administration, South China University of Technology, Guangzhou 510640, ChinaXia LiuOriental Science and Technology College, Hunan Agricultural University, Changsha 410128, ChinaHaiping ShiModern Business and Management Department, Guangdong Construction Polytechnic, Guangzhou 510440, China By using critical point theory, some new criteria are obtained for the existence of a
nontrivial homoclinic orbit to a higher order difference system
containing both many advances and retardations. The proof is based
on the Mountain Pass Lemma in combination with periodic
approximations. Related results in the literature are generalized
and improved.
http://isr-publications.com/jnsa/6000/download-existence-of-solutions-to-boundary-value-problems-for-a-higher-dimensional-difference-systemInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-1901101020171031Some integrability estimates for solutions of the fractional \(p\)-Laplace equation55855592http://dx.doi.org/10.22436/jnsa.010.10.38ENShaoguang ShiDepartment of Mathematics, Linyi University, Linyi 276005, China
For \((\alpha,p)\in(0,1)\times (1,\infty)\), this note focuses on some integrability estimates for solutions of the following Dirichlet problem
\[
\begin{cases}
L_{\alpha,p}u(x)=g(x) \,\,&\hbox{as} \,\,x\in \Omega,\\
u(x)=0 \,\,&\hbox{as} \,\,x\in \mathbb{R}^{n}\backslash \Omega,
\end{cases}
\]
where \(L_{\alpha,p}\) is the fractional \(p\)-Laplace operator. http://isr-publications.com/jnsa/6001/download-some-integrability-estimates-for-solutions-of-the-fractional-p-laplace-equation