Coupled implicit Caputo fractional q-difference systems

Saïd Abbas,Bessem Samet,Mouffak Benchohra,Yong Zhou

doi:10.1186/s13662-019-2433-5

Abstract

This paper deals with some existence, uniqueness, and Ulam stability results for a coupled implicit Caputo fractional q-difference system in Banach and generalized Banach spaces. Some applications are made of some fixed point theorems for the existence and uniqueness of solutions. Next we prove that our problem is generalized Ulam–Hyers–Rassias stable. Some illustrative examples are given in the last section.

Highlights

Fractional differential equations have recently been applied in various areas of engineering, mathematics, physics, and other applied sciences [44]
For some fundamental results in the theory of fractional calculus and fractional differential equations, we refer the reader to the monographs [4,5,6, 33, 42, 47], the paper [46], and the references therein
Considerable attention has been given to the existence of solutions of initial and boundary value problems for fractional differential equations with Caputo fractional derivative [5]

Summary

Introduction

Fractional differential equations have recently been applied in various areas of engineering, mathematics, physics, and other applied sciences [44]. In [1, 2], Abbas et al considered some existence results for some coupled fractional differential systems in generalized Banach spaces. In this paper we discuss the existence and Ulam–Hyers–Rassias stability of solutions for the following coupled implicit fractional q-difference system:

Results

Conclusion