Approximate Controllability of Fractional Semilinear Stochastic System of Order α∈ (1,2

Abstract

A family of dynamical control systems described by nonlinear fractional of order (1,2] stochastic differential equations in Lp spaces is considered. We discussed the approximate controllability of stochastic semilinear fractional control system of order α∈(1,2] under the assumption that the corresponding linear system is approximately controllable. A new set of sufficient conditions for approximate controllability of system are obtained by the theory of strongly continuous α-order cosine family, fixed point theorem, and stochastic analysis techniques. At the end, an example is given to illustrate the theory.