Global attractivity and asymptotic stability of mixed‐order fractional systems

Abstract

This study investigates the asymptotic properties of mixed-order fractional systems. By using the variation of constants formula, properties of real Mittag-Leffler functions, and Banach fixed-point theorem, the authors first propose an explicit criterion guaranteeing global attractivity for a class of mixed-order linear fractional systems. The criterion is easy to check requiring the system's matrix to be strictly diagonally dominant (C1) and elements on its main diagonal to be negative (C2). The authors then show the asymptotic stability of the trivial solution to a non-linear mixed-order fractional system linearised along with its equilibrium point such that its linear part satisfies the conditions (C1) and (C2). Two numerical examples with simulations are given to illustrate the effectiveness of the results over existing ones in the literature.