This study addresses the issue of nonfragile state estimation for memristor-based fractional-order neural networks with hybrid randomly occurring delays. Considering the finite bandwidth of the signal transmission channel, quantitative processing is introduced to reduce network burden and prevent signal blocking and packet loss. In a real-world setting, the designed estimator may experience potential gain variations. To address this issue, a fractional-order nonfragile estimator is developed by incorporating a logarithmic quantizer, which ultimately improves the reliability of the state estimator. In addition, by combining the generalized fractional-order Lyapunov direct method with novel Caputo–Wirtinger integral inequalities, a lower conservative criterion is derived to guarantee the asymptotic stability of the augmented system. At last, the accuracy and practicality of the desired estimation scheme are demonstrated through two simulation examples.

This paper addresses the design of nonfragile state estimators for memristor-based fractional-order neural networks that are subject to stochastic cyber-attacks and hybrid time delays. To mitigate the issue of limited bandwidth during signal transmission, quantitative processing is introduced to reduce network burden and prevent signal blocking. In real network environments, the outputs may be compromised by cyber-attacks, which can disrupt data transmission systems. To better reflect the actual conditions of fractional-order neural networks, a Bernoulli variable is utilized to describe the statistical properties. Additionally, novel conditions are presented to ensure the stochastic asymptotic stability of the augmented error system through a new fractional-order free-matrix-based integral inequality. Finally, the effectiveness of the proposed estimation methods is demonstrated through two numerical simulations.