Approximate controllability of fractional stochastic differential equations driven by Rosenblatt process with non-instantaneous impulses

• In this paper, we consider a new class of impulsive fractional stochastic differential equations driven by Rosenblatt process. • The primary outcomes of this paper are tested by applying the fractional calculus , and Krasnoselskii’s fixed point theorem. • We investigated the approximate controllability results for the proposed system by using a new piecewise control function. • Finally, an illustrative example is presented to demonstrate the validity of the results. In this work, we consider a new class of fractional stochastic differential equations driven by the Rosenblatt process with non-instantaneous impulses. By employing the sectorial operator, fractional calculus, and Krasnoselskii’s fixed point theorem, we investigated the approximate controllability results for the proposed system. Furthermore, an illustrative example is presented to demonstrate the validity of the results.