In this paper, a novel kind of neural networks named fractional-order quaternion-valued bidirectional associative memory neural networks (FQVBAMNNs) is formulated. On one hand, applying Hamilton rules in quaternion multiplication which is essentially non-commutative, the system of FQVBAMNNs is separated into eight fractional-order real-valued systems. Meanwhile, the activation functions are considered to be quaternion-valued linear threshold ones which help to reduce the unnecessary computational complexity. On the other hand, based on fractional-order Lyapunov technology, a new fractional-order derivative inequality is established. Mainly by employing the new inequality technique, constructing three novel Lyapunov-Krasovskii functionals (LKFs) and designing simple linear controllers, the global Mittag-Leffler synchronization problems are investigated and the corresponding criteria are acquired for the system of FQVBAMNNs and its special cases such as fractional-order complex-valued BAM neural networks (FCVBAMNNs) and fractional-order real-valued BAM neural networks (FRVBAMNNs), respectively. Finally, two numerical examples are given to show the effectiveness and availability of the proposed results.

中文翻译：

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基于新不等式的分数阶四元数值BAM神经网络全局Mittag-Leffler同步问题的新方法。

本文提出了一种新型的神经网络，称为分数阶四元数值双向联想记忆神经网络（FQVBAMNNs）。一方面，在四元数乘法中应用汉密尔顿规则，该四元数乘法本质上是不可交换的，FQVBAMNNs系统被分为八个分数阶实数值系统。同时，激活函数被认为是四元数值线性阈值函数，有助于降低不必要的计算复杂性。另一方面，基于分数阶Lyapunov技术，建立了一个新的分数阶导数不等式。主要通过采用新的不等式技术，构造三个新颖的Lyapunov-Krasovskii函数（LKF）并设计简单的线性控制器，研究了全球Mittag-Leffler同步问题，并为FQVBAMNNs系统及其特殊情况（例如分数阶复值BAM神经网络（FCVBAMNNs）和分数阶实值BAM神经网络（FRVBAMNNs））确定了相应的标准）， 分别。最后，给出了两个数值例子来说明所提出的结果的有效性和有效性。