Controllability Criteria for Nonlinear Impulsive Fractional Differential Systems with Distributed Delays in Controls

We establish a class of nonlinear fractional differential systems with distributed time delays in the controls and impulse effects. discuss controllability criteria for both linear systems. The main results required suitable Gramian matrix defined by Mittag–Leffler function, using standard Laplace transform Schauder fixed-point techniques. Further, we provide an illustrative example supported graphical representations to show validity obtained abstract results.