Existence and controllability of impulsive fractional stochastic differential equations driven by Rosenblatt process with Poisson jumps

The goal of this paper is to consider a new class of fractional stochastic differential equations driven by the Rosenblatt process with Poisson jumps and non-instantaneous impulses. By using fractional calculus, stochastic analysis, sectorial operator, and with the help of the fixed-point theorem, the existence of solutions is obtained for the proposed stochastic system. Moreover, we discuss the controllability of the proposed control system. Our main results are well supported by an illustrative example.