Controllability of fractional dynamical systems having multiple delays in control with ψ$$ \psi $$‐Caputo fractional derivative

Abstract

This study investigates the controllability problems for linear and nonlinear fractional control systems with multiple control delays in the context of the ‐Caputo fractional derivative. For the linear case, using the positive definiteness of the Gramian matrix, the necessary and sufficient conditions are obtained. For the nonlinear case, utilizing the iterative technique together with the completeness of the space, sufficient conditions for the existence of a solution are obtained. Just a few examples are included to make theoretical findings easier to grasp, and their respective graphs are plotted.