Approximate Controllability of Fractional Neutral Stochastic Evolution Equations with Nonlocal Conditions

Abstract

In this paper, the approximate controllability of neutral stochastic fractional differential equations involving nonlocal initial conditions is studied. By using Sadovskii’s fixed point theorem with stochastic analysis theory, we derive a new set of sufficient conditions for the approximate controllability of semilinear fractional stochastic differential equations with nonlocal conditions under the assumption that the corresponding linear system is approximately controllable. Finally, an application to a fractional partial stochastic differential equation with nonlocal initial condition is provided to illustrate the obtained theory.