Without decomposing complex-valued systems into real-valued systems, the existence and finite-time stability for discrete fractional-order complex-valued neural networks with time delays are discussed in this paper. First of all, in order to obtain the main results, a new discrete Caputo fractional difference equation is proposed in complex field based on the theory of discrete fractional calculus, which generalizes the fractional-order neural networks in the real domain. Additionally, by utilizing Arzela-Ascoli's theorem, inequality scaling skills and fixed point theorem, some sufficient criteria of delay-dependent are deduced to ensure the existence and finite-time stability of solutions for proposed networks. Finally, the validity and feasibility of the derived theoretical results are indicated by two numerical examples with simulations. Furthermore, we have drawn the following facts: with the lower order, the discrete fractional-order complex-valued neural networks will achieve the finite-time stability more easily.

中文翻译：

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具有时滞的离散分数阶复值神经网络的存在性和有限时间稳定性。

在不将复值系统分解为实值系统的情况下，讨论了具有时滞的离散分数阶复值神经网络的存在性和有限时间稳定性。首先，为了获得主要结果，基于离散分数微积分理论，在复杂领域提出了一个新的离散Caputo分数差分方程，该方程在实域中推广了分数阶神经网络。此外，利用Arzela-Ascoli定理，不等式定标技巧和不动点定理，推导了一些充分的时滞相关准则，以确保所提出网络的解的存在性和时限稳定性。最后，通过两个数值算例与仿真表明了所导出理论结果的有效性和可行性。