Going beyond synchronization of chaos between two integer-order dynamical systems remains a long-standing problem to date, and it was not known how to do it with \(\psi \) -Caputo fractional systems. This paper gives an exhibition by formulating master–slave \(\psi \) -Caputo fractional systems with the implementation of the standard state-feedback control method. We introduce a definition of \(\psi \) -Mittag-Leffler asymptotic stability and develop two synchronization theorems under reasonable Lipschitz assumptions that give local and global results. We address master–slave synchronization between identical Wei systems and Murli-Lakshmanan-Chua circuit systems to show the effectiveness of suggested theoretical validations and convenience for practical implications.
