On a System of ψ-Caputo Hybrid Fractional Differential Equations with Dirichlet Boundary Conditions

Abstract

In this article, we investigate sufficient conditions for the existence and stability of solutions to a coupled system of ψ-Caputo hybrid fractional derivatives of order 1<υ≤2 subjected to Dirichlet boundary conditions. We discuss the existence and uniqueness of solutions with the assistance of the Leray–Schauder alternative theorem and Banach’s contraction principle. In addition, by using some mathematical techniques, we examine the stability results of Ulam–Hyers. Finally, we provide one example in order to show the validity of our results.

Stability of a Solution for a Hybrid Fractional Differential Equation

“…Ulam and Hyers, on the other hand, identified previously unknown types of stability known as Ulam-stability [1]. This example is not exclusive, many similar works can be found in [3,5,11,17,31]. In 2008, Benchohra et al [13], discussed the following boundary value problem…”

Applicability of Darbo’s Fixed Point Theorem on the Existence of a Solution to Fractional Differential Equations of Sequential Type

“…Te study of boundary value problems for equations with nonlinear fractional diferentials has a prominent and important role in the theory of fractional calculus and in the study of physical phenomena through the physical interpretation of boundary conditions. To pass quickly to the practical applications of fractional derivatives in various applied sciences, some valuable works in this feld can be found in [11][12][13][14][15][16][17][18][19].…”

Caputo-hadamard Fractional Differential Equations: Integral Boundary Condition System

“…The challenge of studying the existence and uniqueness solution is the study of its stability. Ulam-Hyers stability (UHS) is the most important types of stability is used in this field ( see [4,10,17,27,28,44], [7,25], [19]) Su [43], studied the existence of solutions for a coupled system of fractional differential equations:…”