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

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.