Abstract In this paper, an integral inequality and the fractional Halanay inequalities with bounded time delays in fractional difference are investigated. By these inequalities, the asymptotical stability conditions of Caputo and Riemann-Liouville fractional difference equation with bounded time delays are obtained. Several examples are presented to illustrate the results.

中文翻译：

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有界时滞分数阶差分方程的渐近稳定性

摘要 本文研究了一个积分不等式和分数差分有界时滞的分数Halanay不等式。通过这些不等式，得到了时滞有界的Caputo和Riemann-Liouville分数阶差分方程的渐近稳定条件。给出了几个例子来说明结果。