Controllability and stability of Prabhakar fractional dynamical systems with a control delay

Abstract This manuscript investigates the controllability of Prabhakar fractional dynamical systems with a single delay in the control function governed by the Prabhakar derivative. This study establishes the controllability conditions for linear delay systems using the Grammian matrix technique. It extends the analysis to nonlinear systems, where controllability is examined through the Schauder fixed‐point theorem. Furthermore, the stability of the nonlinear system involving the Prabhakar derivative is investigated using the concept of Hyers–Ulam stability. To validate the theoretical findings and illustrate their applicability, several numerical examples are presented, along with a comparison that highlights the efficiency of the Prabhakar derivative relative to the Caputo derivative.