Approximate controllability of Sobolev-type fractional functional stochastic integro-differential systems

We discuss the approximate controllability of Sobolev-type fractional functional stochastic differential systems in Hilbert spaces. Using Schauder fixed point theorem, stochastic analysis theory and characteristic solutions operators, we derive a new set of sufficient conditions for the approximate controllability of fractional functional Sobolev-type stochastic integro-differential system under the assumption that the corresponding linear system is approximately controllable. Finally, an example is provided to illustrate the obtained theory.