Controllability of impulsive fractional damped integrodifferential systems with distributed delays

This paper focuses on controllability results for impulsive fractional distributed delay systems with damping behavior, involving the Caputo fractional derivative (CFD) for both linear and integro-differential systems. For linear systems, controllability results are established through the controllability Grammian matrix and employing a control function. Sufficient conditions for the controllability of nonlinear systems are derived using the Schauder fixed point theorem. An example is provided to illustrate the theory.