In this article, the problem of the global Mittag-Leffler synchronization is proposed for a sort of discrete-time fractional-order neural networks (DFNNs) with delays. In the first place, a flesh power law inequality pertaining to fractional difference is constructed by means of integration by parts, Young inequality, and some properties about fractional-order difference. In addition, based on aforesaid inequalities, Lyapunov function theory and properties of nabla Mittag-Leffler function as well as inequality techniques, some plentiful criteria are formed to achieve the global Mittag-Leffler synchronization for the delayed DFNNs via devising novel adaptive controller and delay feedback controller. In the end, numerical modeling is given to demonstrate effectiveness of theoretical verdicts.

在本文中，针对一种具有延迟的离散时间分数阶神经网络（DFNN）提出了全局 Mittag-Leffler 同步问题。首先，利用分部积分、杨不等式以及分数阶差分的一些性质，构造了一个属于分数阶差分的肉幂律不等式。此外，基于上述不等式、Lyapunov 函数理论和 nabla Mittag-Leffler 函数的性质以及不等式技术，通过设计新的自适应控制器和延迟反馈，形成了一些丰富的准则来实现延迟 DFNNs 的全局 Mittag-Leffler 同步。控制器。最后，给出了数值模型来证明理论判断的有效性。