Controllability of Fractional Stochastic Differential Equations With State-Dependent Delay

In this paper, the approximate controllability for a class of nonlinear fractional stochastic differential equations with state-dependent delays in Hilbert space is studied. The result is extended to study the approximate controllability of fractional stochastic systems with state-dependent delays and resolvent operators. A set of sufficient conditions are established to obtain the required result by employing semigroup theory, fixed point technique and fractional calculus. In particular, the approximate controllability of nonlinear fractional stochastic control systems is established under the assumption that the corresponding linear control system is approximately controllable. Also, an example is presented to illustrate the applicability of the obtained theory