The asymptotic stability and synchronization of fractional delayed memristive neural networks with algebraic constraints in Riemann–Liouville sense will be investigated in this article. First, algebraic constraints are introduced for the first time into the existing fractional delayed memristive neural networks, and a new fractional singular delayed memristive neural networks (FSDMNNs) model is presented. Then, within the framework of Filippov’s solution, a less conservative result for the asymptotic stability of FSDMNNs is obtained by Lyapunov–Krasovskii functional. Subsequently, the appropriate feedback scheme and adaptive scheme are designed to synchronize FSDMNNs and two sufficient conditions are acquired. In addition, the results not only address the influence of delays and algebraic constraints, but can also easily detect and synchronize the actual memristive neural networks. Finally, numerical simulations frankly confirm the correctness and validity of the derived results.

本文将研究具有黎曼-刘维尔意义代数约束的分数阶延迟忆阻神经网络的渐近稳定性和同步性。首先，首次将代数约束引入到现有的分数阶延迟忆阻神经网络中，提出了一种新的分数阶奇异延迟忆阻神经网络（FSDMNNs）模型。然后，在 Filippov 解决方案的框架内，通过 Lyapunov-Krasovskii 泛函获得了 FSDMNNs 渐近稳定性的不太保守的结果。随后，设计了适当的反馈方案和自适应方案来同步FSDMNN，并获得了两个充分条件。此外，结果不仅解决了延迟和代数约束的影响，但也可以轻松地检测和同步实际的忆阻神经网络。最后，数值模拟坦率地证实了推导结果的正确性和有效性。