Novel Synchronization Analysis of Fractional-Order Nonautonomous Neural Networks With Mixed Delays

This paper focuses on the global Mittag–Leffler synchronization of fractional-order nonautonomous neural networks with mixed delays (FONANNMD). A time-varying coefficient eÏ t is introduced to capture the nonautonomous dynamics, aligning with real-world time-varying neuron connection weights. A linear feedback controller, integrating proportional, delay, and integral terms, is devised to mitigate mixed delays’ impact on synchronization. Using Caputo fractional derivatives, Mittag–Leffler function properties, and the Lyapunov direct method, sufficient conditions for global synchronization are derived. These conditions are more general than existing ones for autonomous or single-delay systems, ensuring the error system converges to zero in the Mittag–Leffler stability sense. Numerical simulations on 3-dimensional and 4-dimensional neural networks, along with analyses of key parameters (fractional order ξ and delay σ) and convergence metrics (error norms), verify that the proposed controller outperforms traditional proportional feedback in suppressing mixed delays. It also reveals how the fractional order affects synchronization speed.