A note concerning to approximate controllability of Atangana-Baleanu fractional neutral stochastic systems with infinite delay

Abstract

In this paper, we investigate the approximate controllability results of Atangana-Baleanu fractional neutral stochastic systems with infinite delay. Using principles and ideas from stochastic analysis, the theory of multivalued maps, fractional calculus, and Bohnenblust-Karlin fixed point theorem, a new set of sufficient conditions are formulated and proved for the approximate controllability of the fractional stochastic control system. We then apply our findings to the theory of nonlocal conditions. Finally, an example is given to illustrate the theory.