Generalized Mittag-Leffler Input Stability of the Fractional-Order Electrical Circuits

This article addresses new applications of the generalized Mittag-Leffler input stability to the fractional-order electrical circuits. We consider the fractional-order electrical circuits in the context of the generalized Caputo-Liouville derivative. We propose the Lyapunov characterizations of the fractional differential equations. A new numerical discretization, including the fractional differential equations represented by the generalized Caputo derivative, has been successfully applied to the fractional electrical circuits. To support the results, we have proposed the graphics generated by our numerical discretization. The graphics of the solutions have been analyzed and interpreted in the context of generalized Mittag-Leffler input stability and the generalized Mittag-Leffler stability. The generalized Mittag-Leffler input stability is a new stability notion for the fractional differential equations recently introduced in the literature.