Controllability of Nonlinear Fractional Delay Dynamical Systems

This paper is concerned with controllability of nonlinear fractional delay dynamical systems with delay in state variables. The solution representations of fractional delay differential equations have been established by using the Laplace transform technique and the Mittag—Leffler function. Necessary and sufficient conditions for the controllability criteria of linear fractional delay systems are established. Further sufficient condition for the controllability of nonlinear fractional delay dynamical system are obtained by using the fixed point argument. Examples and numerical simulation are presented to illustrate the results.