Abstract
In this paper, we study a type of nonlinear hybrid Delta-difference equations of fractional-order. The main objective is to establish some stability criteria including the Ulam-Hyers stability, generalized Ulam-Hyers stability together with the Mittag-Leffler-Ulam-Hyers stability for the addressed problem. Prior to the stabilization processes, solvability criteria for the existence and uniqueness of solutions are considered. For this purpose, a hybrid fixed point theorem for triple operators and the Banach contraction mapping principle are applied, respectively. For the sake of illustrating the practical impact of the proposed theoretical criteria, we finish the paper with particular examples.