Approximate Controllability of Semilinear Fractional Stochastic System with Nonlocal Conditions

Abstract

This paper deals with the approximate controllability of semilinear fractional stochastic system of order ? ? (1, 2] with nonlocal conditions. By using Sadovskii’s fixed point theorem with fractional calculus and stochastic analysis theory, we derive a new set of sufficient conditions for the approximate controllability of fractional stochastic system with nonlocal conditions under the assumption that the corresponding linear system is approximately controllable. Finally, an application to a fractional stochastic system with nonlocal initial conditions is provided to illustrate the feasibility of the obtained results.