Controllability of Impulsive Nonlinear Fractional Dynamical System with Delays in State and Control

In this paper, the controllability of nonlinear impulsive fractional dynamical system with delays in state and control is analyzed by using a delayed Mittag Leffler (M-L) function. Controllability Grammian matrix is used to establish the controllability of linear system. The sufficient conditions of the considered nonlinear system are derived by utilizing the fixed point techniques. Finally, an example is provided for the illustration of the obtained result.