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.