Global stability of impulsive fractional differential equations

•Impulsive systems of fractional order are investigated.•A new comparison principle using differential inequalities is established.•Impulsive effects on the global stability of solutions are studied.•The Lyapunov function method is extended to impulsive fractional equations.

In the present paper the global stability of systems of impulsive differential equations of fractional order with impulse effect at fixed moments of time is considered. Using piecewise continuous functions of the type of Lyapunov’s functions and a new fractional comparison principle sufficient conditions for various types of global stability are proved.