Discussion on the Optimal Controls Results for Fractional Systems With Atangana–Baleanu Derivative

ABSTRACT In this paper, we present the optimal controls for a system governed by Atangana–Baleanu fractional differential systems in Banach spaces. We verify the existence of the mild solutions through the concepts of fractional calculus, semigroup theory, and Leray–Schauder's fixed point theorem. Likewise, we discuss the existence of optimal controls for the corresponding fractional control system. Furthermore, an example is offered to define the theoretical result.