Controllability Results for $$\psi $$ -Caputo Fractional Differential Systems with Impulsive Effects

Abstract

The main goal of this study is to use the \(\psi \)-Caputo fractional derivative of order \({{\vartheta }} \in (0, 1)\) to construct the criteria for controllability in non-instantaneous impulsive dynamical systems. To obtain the necessary and sufficient conditions for the controllability of linear fractional systems by incorporating the positiveness of the Grammian matrices. To obtain sufficient conditions for controllability criteria for nonlinear systems, we have used Schaefer’s fixed point theorem. To enhance comprehension of the theoretical findings, several numerical examples have been provided.