Controllability of time-varying fractional dynamical systems with distributed delays in control

Abstract This study examines the controllability results in the realm of Caputo fractional derivatives, focusing on time-varying linear and nonlinear fractional dynamical systems with distributed delays in control. In the setting of a linear system, using the Grammian matrix’s positive definiteness makes it possible to ascertain both the necessary and sufficient conditions. Schauder’s fixed point theorem is utilized to outline the sufficient conditions for establishing the controllability of time-varying nonlinear fractional dynamical systems. In addition to that, the paper discusses the controllability of a nonlinear integrodifferential system for a particular case. A few examples and the graphs that correspond to them are shown here to make it easier to conceptualize the conclusions of the theoretical discussion.