International Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-190111820180604Cylindrical Carleman's formula of subharmonic functions and its application947952http://dx.doi.org/10.22436/jnsa.011.08.01ENLei QiaoSchool of Mathematics and Information Science, Henan University of Economics and Law, Zhengzhou 450046, ChinaOur aim in this paper is to prove the cylindrical Carleman's formula for subharmonic functions in a truncated cylinder. As an
application, we prove that if the positive part of a harmonic function in a cylinder satisfies a slowly growing condition, then
its negative part can also be dominated by a similar slowly growing condition, which
improves some classical results about harmonic functions in a cylinder. http://isr-publications.com/jnsa/7106/download-cylindrical-carlemans-formula-of-subharmonic-functions-and-its-applicationInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-190111820180604Ulam-Hyers stability of fractional impulsive differential equations953959http://dx.doi.org/10.22436/jnsa.011.08.02ENYali DingSchool of Mathematics and Statistics, Beijing Institute of Technology, Beijing 100081, P. R. ChinaIn this paper, we first prove the existence and uniqueness for a fractional differential equation with time delay and finite impulses on a compact interval. Secondly, Ulam-Hyers stability of the equation is established by Picard operator and abstract Gronwall's inequality. http://isr-publications.com/jnsa/7107/download-ulam-hyers-stability-of-fractional-impulsive-differential-equationsInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-190111820180607Iterative methods for solving the split common fixed point problem of demicontractive mappings in Hilbert spaces960970http://dx.doi.org/10.22436/jnsa.011.08.03ENChunxiang ZongDepartment of Mathematics, Nanchang University, Nanchang 330031, P. R. ChinaYuchao TangDepartment of Mathematics, Nanchang University, Nanchang 330031, P. R. ChinaThe split common fixed point problem was proposed in recent years
which required to find a common fixed point of a family of mappings
in one space whose image under a linear transformation is a common
fixed point of another family of mappings in the image space. In
this paper, we study two iterative algorithms for solving this split
common fixed point problem for the class of demicontractive mappings
in Hilbert spaces. Under mild assumptions on the parameters, we
prove the convergence of both iterative algorithms. As a consequence, we obtain new convergence
theorems for solving the split
common fixed point problem for the class of directed mappings. We compare the performance of the proposed iterative
algorithms with the existing iterative algorithms and conclude from the numerical experiments that our iterative algorithms converge faster than
these existing iterative algorithms in terms of iteration numbers.http://isr-publications.com/jnsa/7119/download-iterative-methods-for-solving-the-split-common-fixed-point-problem-of-demicontractive-mappings-in-hilbert-spacesInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-190111820180609The \(q\)-Stirling numbers of the second kind and its applications971983http://dx.doi.org/10.22436/jnsa.011.08.04ENMin-Soo KimDivision of Mathematics, Science, and Computers, Kyungnam University, 7(Woryeong-dong) kyungnamdaehak-ro, Masanhappo-gu, Changwon-si, Gyeongsangnam-do 51767, Republic of KoreaDaeyeoul KimDepartment of Mathematics and Institute of Pure and Applied Mathematics, Chonbuk National University, Jeonju-si 54896, Republic of KoreaThe study of \(q\)-Stirling numbers of the second kind began with Carlitz [L. Carlitz, Duke Math. J., \(\textbf{15}\) (1948), 987--1000] in 1948.
Following Carlitz, we derive some identities and relations related to \(q\)-Stirling numbers of the second kind
which appear to be either new or else new ways of expressing older ideas more comprehensively.http://isr-publications.com/jnsa/7124/download-the-q-stirling-numbers-of-the-second-kind-and-its-applicationsInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-190111820180609Fractional integral associated to Schrödinger operator on the Heisenberg groups in central generalized Morrey spaces984993http://dx.doi.org/10.22436/jnsa.011.08.05ENAhmet ErogluNigde Omer Halisdemir University, Department of Mathematics, Nigde, TurkeyTahir GadjievInstitute of Mathematics and Mechanics of NAS of Azerbaijan, AZ1141 Baku, AzerbaijanFaig NamazovBaku State University, AZ1141 Baku, AzerbaijanLet \(L=-\Delta_{\mathbb{H}_n}+V\) be a Schrödinger operator on the Heisenberg groups \(\mathbb{H}_n\), where the non-negative potential \(V\) belongs to the reverse Hölder class \(RH_{Q/2}\)
and \(Q\) is the homogeneous dimension of \(\mathbb{H}_n\). Let \(b\) belong to a new \(BMO_{\theta}(\mathbb{H}_n,\rho)\) space, and let \({\cal I}_{\beta}^{L}\) be the fractional integral operator associated with \(L\).
In this paper, we study the boundedness of the operator \({\cal I}_{\beta}^{L}\) and its commutators \([b,{\cal I}_{\beta}^{L}]\) with \(b \in BMO_{\theta}(\mathbb{H}_n,\rho)\)
on central generalized Morrey spaces \(LM_{p,\varphi}^{\alpha,V}(\mathbb{H}_n)\) and generalized Morrey spaces \(M_{p,\varphi}^{\alpha,V}(\mathbb{H}_n)\) associated with Schrödinger operator.
We find the sufficient conditions on the pair \((\varphi_1,\varphi_2)\) which ensures the boundedness of the operator \({\cal I}_{\beta}^{L}\)
from \(LM_{p,\varphi_1}^{\alpha,V}(\mathbb{H}_n)\) to \(LM_{q,\varphi_2}^{\alpha,V}(\mathbb{H}_n)\) and from \(M_{p,\varphi_1}^{\alpha,V}(\mathbb{H}_n)\) to \(M_{q,\varphi_2}^{\alpha,V}(\mathbb{H}_n)\), \(1/p-1/q=\beta/Q\).
When \(b\) belongs to \(BMO_{\theta}(\mathbb{H}_n,\rho)\) and \((\varphi_1,\varphi_2)\) satisfies some conditions, we also show that the commutator operator \([b,{\cal I}_{\beta}^{L}]\) is bounded
from \(LM_{p,\varphi_1}^{\alpha,V}(\mathbb{H}_n)\) to \(LM_{q,\varphi_2}^{\alpha,V}(\mathbb{H}_n)\) and from \(M_{p,\varphi_1}^{\alpha,V}\) to \(M_{q,\varphi_2}^{\alpha,V}\), \(1/p-1/q=\beta/Q\).http://isr-publications.com/jnsa/7125/download-fractional-integral-associated-to-schrodinger-operator-on-the-heisenberg-groups-in-central-generalized-morrey-spacesInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-190111820180611Mathematical modeling of the smoking dynamics using fractional differential equations with local and nonlocal kernel9941014http://dx.doi.org/10.22436/jnsa.011.08.06ENV. F. Morales-DelgadoFacultad de Matematicas, Universidad Autonoma de Guerrero. Av. Lázaro Cárdenas S/N, Cd. Universitaria. Chilpancingo, Guerrero, MexicoJ. F. Gómez-AguilarCONACyT-Tecnológico Nacional de México/CENIDET, Interior Internado Palmira S/N, Col. Palmira, C.P. 62490, Cuernavaca, Morelos, MexicoM. A.Taneco-HernándezFacultad de Matematicas, Universidad Autonoma de Guerrero. Av. Lázaro Cárdenas S/N, Cd. Universitaria. Chilpancingo, Guerrero, MexicoR. F.Escobar-JiménezTecnológico Nacional de México/CENIDET, Interior Internado Palmira S/N, Col. Palmira, C.P. 62490, Cuernavaca, Morelos, MexicoV. H. Olivares-PeregrinoTecnológico Nacional de México/CENIDET, Interior Internado Palmira S/N, Col. Palmira, C.P. 62490, Cuernavaca, Morelos, MexicoIn this paper, we analyze the fractional modeling of the giving up the smoking using the definitions of Liouville-Caputo and Atangana-Baleanu-Caputo fractional derivatives. Applying the homotopy analysis method and the Laplace transform with polynomial homotopy, the analytical solution of the smoking dynamics has obtained. Furthermore, using an iterative scheme by the Laplace transform, and the Atangana-Baleanu fractional integral, special solutions of the model are obtained. Uniqueness and existence of the solutions by the fixed-point theorem and Picard-Lindelof approach are studied. Finally, some numerical simulations are carried out for illustrating the results obtained.http://isr-publications.com/jnsa/7131/download-mathematical-modeling-of-the-smoking-dynamics-using-fractional-differential-equations-with-local-and-nonlocal-kernel