Stability analysis for generalized fractional differential systems and applications

Abstract

Abstract This paper shows solicitude for the stability analysis issue of a class of generalized fractional differential systems via fractional comparison principle and Lyapunov direct method. With the concept of (Generalized) Mittag-Leffler (M-L) stability given, we first establish a new framework to consider the global M-L stability of generalized fractional differential systems with or without time-delay, in which new stability criterion is achieved by some novel differential inequalities satisfied by the fractional derivative of Lyapunov functions. Second, through the employment of less conservative comparison principle for the generalized fractional system, a sufficient theorem for the (Generalized) M-L stability is derived. Third, a generalized fractional memristor-based impulsive neural network is investigated to illustrate the proposed stability theory, this model is more general which includes a memristor-based Caputo fractional neural network or common Hopfield neural network as special cases. In the end, two simple numerical examples are listed to affirm the theoretical findings.