Stability analysis for a class of nabla (q; h)-fractional difference equations

Abstract

This paper investigates stability of the nabla (q; h) -fractional difference equations. Asymptotic stability ofthe special nabla (q; h) -fractional difference equations are discussed. Stability theorems for discrete fractional Lyapunovdirect method are proved. Furthermore, we give some new lemmas (including important comparison theorems) relatedto the nabla (q; h) -fractional difference operators that allow proving the stability of the nabla (q; h) -fractional differenceequations, by means of the discrete fractional Lyapunov direct method, using Lyapunov functions. Some examples aregiven to illustrate these results.