Controllability Results for Impulsive Atangana-Baleanu Fractional Stochastic Differential Systems with Second-Order Hermite Process

Abstract

This paper develops a new class of impulsive Atangana-Baleanu fractional stochastic differential systems with the Rosenblatt process, which is a Hermite process of order two with long-range dependence and stationary increments properties. Firstly, we established the existence of solutions to the considered problem by using the fixed point technique, resolvent family, and fractional calculus. Then, we discussed the controllability results for the proposed system. Finally, an illustrative example is given to demonstrate the obtained results.