Controllability of nonlinear stochastic fractional systems with Lévy Noise

In this paper we study the controllability of linear and nonlinear stochastic fractional systems driven by Lévy noise. Here we use the Lévy-Itô decomposition of an arbitrary Lévy 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.