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.

中文翻译：

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不确定分数差分方程的有限时间稳定性

不确定的分数差分方程可以优选地描述在不确定环境中具有记忆效应和离散特征的系统的行为。因此研究其稳定性具有重要意义。在本文中，几乎可以肯定地引入不确定分数阶差分方程的有限时间稳定性的概念。然后，由Mittag–Leffler函数表示有限时间稳定性定理，并由有限时间上的广义Gronwall不等式证明。最后给出一些例子来说明我们的结果的有效性。