Analysis of switched coupled impulsive fractional stochastic differential systems using Atangana-Baleanu derivatives

Abstract

In this paper, we consider a class of implicit switched coupled systems of Atangana-Baleanu (A-B) fractional stochastic differential equations with non-instantaneous impulses and nonlocal conditions. Techniques from nonlinear functional analysis are employed to establish sufficient conditions for the existence and uniqueness of solutions. Furthermore, the stability of the model is investigated under various concepts, including Ulam-Hyers, generalised Ulam-Hyers, Ulam-Hyers-Rassias, and generalised Ulam-Hyers-Rassias stability, using Banach's fixed point theorem. To illustrate and validate the theoretical results, a concrete example with graphical representations is provided. The findings demonstrate that the proposed method is effective and well suited for addressing fractional stochastic problems in engineering, technology, and physics, particularly when modeled with the A-B fractional derivative.