Asymptotic stability of nonlinear neutral fractional difference equations

Hamid Boulares,  et al.

Volume 8 No 4,  2017

Mathematics in Engineering, Science and Aerospace (MESA)

Abstract

In this paper, we give sufficient conditions to guarantee the asymptotic stability of the solutions to a kind of nonlinear neutral fractional difference equations with the Caputo like difference operator of order α (0<α<1). By using the Krasnoselskii's fixed point theorem and discrete Arzela-Ascoli's theorem, we establish new results on the asymptotic stability of the solutions, which include and improve some related results in the literature.