Finite-time stability of uncertain fractional difference equations

Uncertain fractional difference equations may preferably describe the behavior of the systems with the memory effect and discrete feature in the uncertain environment. So it is of great significance to investigate their stability. In this paper, the concept of finite-time stability almost surely for uncertain fractional difference equations is introduced. A finite-time stability theorem is then stated by Mittag–Leffler function and proved by a generalized Gronwall inequality on a finite time. Some examples are finally presented to illustrate the validity of our results.