Approximate controllability of Atangana- Baleanu fractional stochastic differential systems with non-Gaussian process and impulses

This paper aims to investigate a new class of Atangana-Baleanu fractional stochastic differential systems under the influence of the Rosenblatt process and non-instantaneous impulses. We analyze the existence and uniqueness of piecewise continuous mild solutions by using the fixed point method, fractional calculus, and resolvent family. Further, we define a new piecewise control function and investigate the approximate controllability results for the proposed problem. Finally, the main results are validated with the aid of an example.