Existence and Stability for a Coupled Hybrid System of Fractional Differential Equations with Atangana–Baleanu–Caputo Derivative

Abstract

The aim of this article is to investigate a coupled hybrid system of fractional differential equations with the Atangana–Baleanu–Caputo derivative which contains a Mittag–Leffler kernel function in its kernel. We firstly apply the Dhage fixed point principle to obtain the existence of mild solutions. Then, we study the Ulam–Hyers stability of the introduced fractional coupled hybrid system. Finally, an example is presented to exhibit the validity of our results.