Controllability for Time-dependent Neutral Stochastic Functional Differential Equations with Rosenblatt Process and Impulses

In this paper we consider the controllability of certain class of non-autonomous impulsive neutral evolution stochastic functional differential equations, with time varying delays, driven by a Rosenblatt process, in a Hilbert space. Sufficient conditions for controllability are obtained by employing a fixed point approach. A practical example is provided to illustrate the viability of the abstract result of this work.