This paper proposes two methods to investigate the problem of finite-time Mittag-Leffler synchronization for the systems of fractional-order quaternion-valued neural networks (FQVNNs) with two kinds of activation functions, respectively. Generally, the first method mainly reflects in the new establishment of Lyapunov-Krasovskii functionals (LKFs) and the novel application of a new fractional-order derivative inequality which contains and exploits the wider coefficients with more values. Meanwhile, the second one is embodied in the comprehensive development of both the norm comparison rules and the generalized Gronwall-Bellman inequality with the help of Laplace transform of Mittag-Leffler function. Thanks to the above two methods, the flexible synchronization criteria are easily and separately obtained for the studied four systems of FQVNNs with general activation functions and linear threshold ones. Finally, two numerical simulations are given to demonstrate the feasibility and effectiveness of the newly proposed approaches.

本文提出了两种方法分别研究具有两种激活函数的分数阶四元数值神经网络（FQVNN）系统的有限时间Mittag-Leffler同步问题。通常，第一种方法主要反映在Lyapunov-Krasovskii泛函（LKFs）的新建立和新的分数阶导数不等式的新应用中，该分数阶不等式包含并利用了具有更多值的更宽的系数。同时，第二个体现在借助Mittag-Leffler函数的Laplace变换对范式比较规则和广义Gronwall-Bellman不等式的综合发展中。由于以上两种方法，对于四个具有通用激活函数和线性阈值的FQVNNs系统，可以轻松，分别地获得灵活的同步标准。最后，通过两个数值模拟来证明新方法的可行性和有效性。