Mittag-Leffler stability for a new coupled system of fractional-order differential equations with impulses

Abstract

This paper is devoted to investigation of the Mittag-Leffler stability problem for a new coupled system of fractional-order differential equations with impulses on networks. By using the direct graph theory, a new coupled model with two fractional-order impulsive equations on each vertex is constructed, and the related Lyapunov function is presented. By the Lyapunov direct method, sufficient conditions are derived to ensure the equilibrium point of the coupled fractional-order impulsive model is globally Mittag-Leffler stable. Our new results show a relation between the stability criteria and some topology property of the system. Finally, a numerical example is provided to illustrate the effectiveness of our results.