Controllability of Prabhakar Fractional Dynamical Systems

In this manuscript, we focus on the investigation of controllability results in various types of Prabhakar fractional dynamical systems (FDSs). We establish sufficient and necessary conditions for the controllability of linear Prabhakar FDS. Additionally, we explore sufficient conditions for the controllability of nonlinear Prabhakar FDS, nonlinear integro-differential Prabhakar FDS, and nonlinear neutral Prabhakar FDS using the Schauder fixed point theorem. For the controllability of nonlinear Prabhakar PDSs, we assume that the nonlinear function is continuous instead of Lipschitz continuous. The solution of the neutral Prabhakar FDS is determined by applying the Laplace transform. Finally, we provide illustrative examples to validate and demonstrate the applicability of the obtained results.