Xiang LIU, Baoguo JIA, Lynn ERBE, Allan PETERSON

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

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.

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