A New Class of Coupled Systems of Nonlinear Hyperbolic Partial Fractional Differential Equations in Generalized Banach Spaces Involving the ψ–Caputo Fractional Derivative

Zidane Baitiche,Choukri Derbazi,Yong Zhou,Mouffak Benchohra

doi:10.3390/sym13122412

Abstract

The current study is devoted to investigating the existence and uniqueness of solutions for a new class of symmetrically coupled system of nonlinear hyperbolic partial-fractional differential equations in generalized Banach spaces in the sense of ψ–Caputo partial fractional derivative. Our approach is based on the Krasnoselskii-type fixed point theorem in generalized Banach spaces and Perov’s fixed point theorem together with the Bielecki norm, while Urs’s approach was used to prove the Ulam–Hyers stability of solutions of our system. Finally, some examples are provided in order to illustrate our theoretical results.

Highlights

During the last twenty years, fractional differential equations have gained considerable attention in various fields of applied mathematics and engineering
A generalization of derivatives of both Caputo and Caputo–Hadamard was provided by Almeida in [10]. He named it as a ψ–Caputo fractional derivative
We present some basic definitions and classical results about fractional calculus, matrix analysis, and fixed-point theorems that are be used throughout this paper

Summary

Introduction

During the last twenty years, fractional differential equations have gained considerable attention in various fields of applied mathematics and engineering. For some recent results on the existence and stability of solutions for a coupled system of fractional differential equations involving different forms of fractional derivatives, we refer the reader to [23,24,25,26,27,28]. Reason, in this paper, we study the existence, uniqueness, and the Ulam–Hyers stability of solutions for the following coupled system with symmetry: (

Results

Conclusion