Controllability of Nonlinear Stochastic Fractional Systems with L´evy Noise

Abstract

In this paper we study the controllability of linear and nonlinear stochastic fractional systems driven by Levy noise. Here we use the Levy-Ito decomposition of an arbitrary Levy process into Brownian and Poisson parts. The necessary and sufficient conditions for controllability of the linear system is obtained. Also, the nonlinear system is shown controllable under the assumption that the corresponding linear system is controllable and using the Banach contraction principle.