Impulsive Coupled System of Fractional Differential Equations with Caputo–Katugampola Fuzzy Fractional Derivative

Leila Sajedi,Hassen Aydi,Nasrin Eghbali,Xiaolong Qin

doi:10.1155/2021/7275934

Abstract

In this article, we investigate the existence, uniqueness, and different kinds of Ulam–Hyers stability of solutions of an impulsive coupled system of fractional differential equations by using the Caputo–Katugampola fuzzy fractional derivative. We applied the Perov-type fixed point theorem to prove the existence and uniqueness of the proposed system. Furthermore, the Ulam–Hyers–Rassias stability and Ulam–Hyers–Rassias–Mittag-Leffler’s stability results for the given system are discussed.

Highlights

Fractional differential equations have become powerful tools for describing the mathematical modeling of systems. ey have been widely used in modeling real-world phenomena and various fields such as economics, biology, mechanics, bioengineering, physics, and other applied sciences
Almeida in [4] suggested a Caputo fractional derivative of one function to another function. e generalization of the Riemann–Liouville and Caputo derivatives has presented the effect of using it in mathematical physics equations
Motivated by the aforementioned works, in this paper, we study the existence, uniqueness, and Ulam-type stability of the following coupled system of fractional differential equations of the form:

Summary

Introduction

Fractional differential equations have become powerful tools for describing the mathematical modeling of systems. ey have been widely used in modeling real-world phenomena and various fields such as economics, biology, mechanics, bioengineering, physics, and other applied sciences. Is theory, as well as the benefits of fractional calculus, has attracted numerous mathematicians so that the research studies about the existence, uniqueness, and stability have developed; for example, Allahviranloo et al [9] applied the generalized Hukuhara Caputo differentiability to investigate the existence and uniqueness of the solution for fuzzy fractional differential equations. For more recent developments about this concept, [12,13,14,15,16,17,18,19] and the references therein are some papers that include basic outcomes in the theory of fuzzy fractional differential equations and the method for investigating numerical solutions of them. Motivated by the aforementioned works, in this paper, we study the existence, uniqueness, and Ulam-type stability of the following coupled system of fractional differential equations of the form:.

Preliminaries

Conclusion