Approximate Controllability of Retarded Impulsive Stochastic Integro-Differential Equations Driven by Fractional Brownian Motion

Abstract

In this paper,  we investigate the approximate controllability of  retarded impulsive stochastic integro-differential equations driven by fractional Brownian motion(fBm) in Hilbert space. With the help of  the resolvent operators, the fixed-point theorem, stochastic analysis and methods of controllability theory,  a new set of sufficient conditions for approximate controllability of  the integro-differential equations are formulated and proven.  An example is provided to illustrate the obtained theory.