CONTROLLABILITY OF SEMILINEAR NEUTRAL STOCHASTIC INTEGRODIFFERENTIAL EVOLUTION SYSTEMS WITH FRACTIONAL BROWNIAN MOTION

Abstract

This paper focuses on the approximate controllability of semilinear neutral stochastic integrodifferential systems with fractional Brownian motion in a Hilbert space. The theory of analytic resolvent operators of linear neutral integrodifferential equations and the Banach fixed point theorem are employed to obtain the main results. In order to improve the regularity of solutions, the theory of fractional powers and the $\alpha$-norm are also utilized to discuss the problem. An example is presented in the end to illustrate the applications of the obtained results.