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.