Controllability of a Stochastic Neutral Functional Differential Equation Driven by a fBm

Abstract

In this paper, we consider a class of Sobolev-type fractional neutral stochastic differential equations driven by fractional Brownian motion with infinite delay in a Hilbert space. When 1 H α > − , by the technique of Sadovskii's fixed point theorem, stochastic calculus and the methods adopted directly from deterministic control problems, we study the approximate controllability of the stochastic system.