This paper is concerned with the finite-time projective synchronization problem of fractional-order memristive neural networks (FMNNs) with mixed time-varying delays. Firstly, under the frame of fractional-order differential inclusion and the set-valued map, several criteria are derived to ensure finite-time projective synchronization of FMNNs. Meanwhile, three properties are established to deal with different forms of the finite-time fractional differential inequation, which greatly extend some results on estimation of settling time of FMNNs. In addition to the traditional Lyapunov function with 1-norm form in Theorem 1, a more general and flexible Lyapunov function based on p-norm is constructed in Theorem 2 to analyze the finite-time projective synchronization problem, and the estimation of settling time has been verified less conservative than previous results. Finally, numerical examples are provided to demonstrate the effectiveness of the derived theoretical results.

中文翻译：

---

具有混合时变时滞的分数阶忆阻神经网络的有限时间投影同步

本文涉及具有混合时变时滞的分数阶忆阻神经网络（FMNN）的有限时间射影同步问题。首先，在分数阶微分包含和集值映射的框架下，导出了确保FMNNs有限时间投影同步的几个准则。同时，建立了三种性质来处理有限时间分数阶微分不等式的不同形式，这大大扩展了FMNNs建立时间估计的一些结果。除了定理1中具有1范数形式的传统Lyapunov函数之外，在定理2中还构造了基于p范数的更通用，更灵活的Lyapunov函数，以分析有限时间射影同步问题，并且已经证明建立时间的估计比以前的结果保守。最后，通过数值算例证明了所导出理论结果的有效性。