Controllability and stability of fractional stochastic functional systems driven by Rosenblatt process

Abstract

In this paper, we investigate the controllability and exponential stability results for a class of nonlinear neutral stochastic functional differential control systems in the presence of infinite delay driven by Rosenblatt process in real separable Hilbert spaces. Firstly, by using stochastic analysis approach, fractional calculus theory and a fixed point technique, we prove the controllability result for the mild solutions of the nonlinear control systems with the condition that the associated linear system is controllable. Secondly, we discuss the exponential stability of mild solutions of the nonlinear neutral stochastic differential systems driven by Rosenblatt process. Finally, an example is presented to illustrate the obtained theory.