Atangana–Baleanu Semilinear Fractional Differential Inclusions With Infinite Delay: Existence and Approximate Controllability

Abstract

Abstract The main focus of this paper is centered around approximate controllability results of Atangana–Baleanu fractional differential systems with infinite delay. Using principles and ideas from the theory of multivalued maps, fractional calculus, and Bohnenblust–Karlin fixed point techniques, the key findings are established. We begin by emphasizing the existence of mild solutions, and then demonstrate the approximate controllability of the Atangana–Baleanu fractional control system. We then apply our findings to the theory of the neutral system.