Approximate Controllability of Nonlinear Stochastic Integrodifferential Third Order Dispersion System

Abstract

In this work, a class of control systems governed by the stochastic nonlinear integrodifferential third order dispersion equations in Hilbert spaces are considered. The existence of mild solutions of stochastic nonlinear integrodifferential third order dispersion equations are proved using fixed point theory, semigroup properties and stochastic analysis techniques. A new set of sufficient conditions are formulated which guarantees the approximate controllability of the main problem. An example is provided to illustrate the application of the main result.