Lyapunov functions for Riemann–Liouville-like fractional difference equations

摘要

Discrete memory effects are introduced by fractional difference operators. Asymptotic stabilities of nonlinear fractional difference equations are investigated in this paper. A linear scalar fractional difference equality is utilized. Lyapunov second direct method is proposed for nonlinear discrete fractional systems. Asymptotic stability conditions are provided and some examples are given.