Stability Results for a Coupled System of Impulsive Fractional Differential Equations

Akbar Zada,Shaheen Fatima,Yujun Cui,Zeeshan Ali,Jiafa Xu

doi:10.3390/math7100927

Abstract

In this paper, we establish sufficient conditions for the existence, uniqueness and Ulam–Hyers stability of the solutions of a coupled system of nonlinear fractional impulsive differential equations. The existence and uniqueness results are carried out via Banach contraction principle and Schauder’s fixed point theorem. The main theoretical results are well illustrated with the help of an example.

Highlights

Fractional differential equations (FDEs) provide an excellent tool for the description of memory and hereditary properties of different processes and materials
Inspired from the above discussion, in this article, we study the existence, uniqueness and stability analysis of a coupled system of nonlinear FDEs with impulses of the form:
We give some basic definitions of fractional calculus that will be used throughout the article

Summary

Introduction

Fractional differential equations (FDEs) provide an excellent tool for the description of memory and hereditary properties of different processes and materials. FDEs with different boundary conditions; see [32–40] and references cited therein In fields such as numerical analysis, optimization theory, and nonlinear analysis, we mostly deal with the approximate solutions and we need to check how close these solutions are to the actual solutions of the related system. For this purpose, many approaches can be used, but the approach of Ulam–Hyers stability is a simple and easy one. Inspired from the above discussion, in this article, we study the existence, uniqueness and stability analysis of a coupled system of nonlinear FDEs with impulses of the form:.

Background

Main Results

Ulam–Hyers Stability

Example

Conclusions