Controllability of Nonlinear Fractional Langevin Systems

In this paper, we first derive the solution representation of fractional Langevin differential equation represented by the fractional differential coefficient in the sense of Caputo fractional derivative in terms of Mittag-Leffler function. Based on this solution representation, controllability of linear fractional Langevin dynamical systems is studied by using Grammian matrix. Sufficient conditions for the controllability of the nonlinear system are established by using the Schauder’s fixed point theorem. An example is given to verify the results.