This paper studies one type of delayed memristor-based fractional-order neural networks (MFNNs) on the finite-time stability problem. By using the method of iteration, contracting mapping principle, the theory of differential inclusion, and set-valued mapping, a new criterion for the existence and uniqueness of the equilibrium point which is stable in finite time of considered MFNNs is established when the order $ \alpha $ satisfies $ {0< \alpha < 1}$ . Then, when ${1< \alpha < 2}$ , on the basis of generalized Gronwall inequality and Laplace transform, a sufficient condition ensuring the considered MFNNs stable in finite time is given. Ultimately, simulation examples are proposed to demonstrate the validity of the results.

中文翻译：

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基于延迟忆阻器的分数阶神经网络的有限时间稳定性

本文研究了一种基于时滞忆阻器的分数阶神经网络（MFNN）的有限时间稳定性问题。利用迭代方法，压缩映射原理，微分包含理论和集值映射，建立了考虑的MFNNs在有限时间内稳定的平衡点的存在和唯一性的新准则。 $ \ alpha $ 满足 $ {0 <\ alpha <1} $ 。然后，当 $ {1 <\ alpha <2} $ 在广义Gronwall不等式和Laplace变换的基础上，给出了确保所考虑的MFNN在有限时间内稳定的充分条件。最终，提出了仿真示例以证明结果的有效性。