In this paper, finite-time stability of fractional delay difference equations with discrete Mittag-Leffler kernel are studied. Firstly, we establish a new generalized Gronwall inequality in sense of Atangana-Baleanu fractional difference sum operator. Then, based on this new generalized Gronwall inequality and the method of steps, finite-time stability criteria of fractional delay difference equations with discrete Mittag-Leffler kernel are induced respectively. Finally, examples are presented to illustrate the validity of main results.

中文翻译：

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ABC型分数延迟差分方程的有限时间稳定性

本文研究了离散Mittag-Leffler核分数阶时滞差分方程的有限时间稳定性。首先，我们在Atangana-Baleanu分数差分和算子意义上建立了一个新的广义Gronwall不等式。然后，基于这个新的广义Gronwall不等式和步长法，分别推导出具有离散Mittag-Leffler核的分数延迟差分方程的有限时间稳定性判据。最后，通过实例说明主要结果的有效性。