ULAM-HYERS-RASSIAS STABILITY AND EXISTENCE OF SOLUTIONS TO NONLINEAR FRACTIONAL DIFFERENCE EQUATIONS WITH MULTIPOINT SUMMATION BOUNDARY CONDITION

doi:10.1007/s10473-020-0219-1

数学物理学报(英文版) ›› 2020, Vol. 40 ›› Issue (2): 589-602.doi: 10.1007/s10473-020-0219-1

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ULAM-HYERS-RASSIAS STABILITY AND EXISTENCE OF SOLUTIONS TO NONLINEAR FRACTIONAL DIFFERENCE EQUATIONS WITH MULTIPOINT SUMMATION BOUNDARY CONDITION

Syed Sabyel HAIDER, Mujeeb Ur REHMAN

School of Natural Sciences, National University of Sciences and Technology, H-12 Islamabad, 44000, Pakistan

收稿日期:2018-10-26 修回日期:2019-04-25 出版日期:2020-04-25 发布日期:2020-05-26
通讯作者: Syed Sabyel HAIDER E-mail:rediahleybas@gmail.com
作者简介:Mujeeb Ur REHMAN,E-mail:mujeeburrehman345@yahoo.com

ULAM-HYERS-RASSIAS STABILITY AND EXISTENCE OF SOLUTIONS TO NONLINEAR FRACTIONAL DIFFERENCE EQUATIONS WITH MULTIPOINT SUMMATION BOUNDARY CONDITION

Syed Sabyel HAIDER, Mujeeb Ur REHMAN

School of Natural Sciences, National University of Sciences and Technology, H-12 Islamabad, 44000, Pakistan

Received:2018-10-26 Revised:2019-04-25 Online:2020-04-25 Published:2020-05-26
Contact: Syed Sabyel HAIDER E-mail:rediahleybas@gmail.com

摘要/Abstract

摘要： The purpose of this study is to acquire some conditions that reveal existence and stability for solutions to a class of difference equations with non-integer order μ∈ (1, 2]. The required conditions are obtained by applying the technique of contraction principle for uniqueness and Schauder's fixed point theorem for existence. Also, we establish some conditions under which the solution of the considered class of difference equations is generalized Ulam-Hyers-Rassias stable. Example for the illustration of results is given.

关键词: Fractional difference equation, Green's function, existence and uniqueness, Ulam-Hyers-Rassias stability, summation boundary condition

Abstract: The purpose of this study is to acquire some conditions that reveal existence and stability for solutions to a class of difference equations with non-integer order μ∈ (1, 2]. The required conditions are obtained by applying the technique of contraction principle for uniqueness and Schauder's fixed point theorem for existence. Also, we establish some conditions under which the solution of the considered class of difference equations is generalized Ulam-Hyers-Rassias stable. Example for the illustration of results is given.

Key words: Fractional difference equation, Green's function, existence and uniqueness, Ulam-Hyers-Rassias stability, summation boundary condition

中图分类号:

39A30

Syed Sabyel HAIDER, Mujeeb Ur REHMAN. ULAM-HYERS-RASSIAS STABILITY AND EXISTENCE OF SOLUTIONS TO NONLINEAR FRACTIONAL DIFFERENCE EQUATIONS WITH MULTIPOINT SUMMATION BOUNDARY CONDITION[J]. 数学物理学报(英文版), 2020, 40(2): 589-602.

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ULAM-HYERS-RASSIAS STABILITY AND EXISTENCE OF SOLUTIONS TO NONLINEAR FRACTIONAL DIFFERENCE EQUATIONS WITH MULTIPOINT SUMMATION BOUNDARY CONDITION

ULAM-HYERS-RASSIAS STABILITY AND EXISTENCE OF SOLUTIONS TO NONLINEAR FRACTIONAL DIFFERENCE EQUATIONS WITH MULTIPOINT SUMMATION BOUNDARY CONDITION

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