Abstract
The idea behind this study is to investigate the controllability of dynamical systems in terms of the ψ-Caputo fractional derivative. The Grammian matrix is used to get at necessary and sufficient controllability requirements for linear systems, which are characterized by the Mittag-Leffler functions, while the fixed point approach is used to arrive at adequate controllability criteria for nonlinear systems. The novelty of this research is to inquire into the controllability concepts by utilizing the ψ-Caputo fractional derivative. Since ψ-Caputo fractional derivatives have the advantage of capturing memory effects as well as increasing the accuracy of anticipating real-world scenarios. A few numerical examples are offered to help better understand the theoretical results.
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