Mittag-Leffler projective synchronization of Caputo fractional-order reaction–diffusion memristive neural networks with multi-type time delays

Neural synchronization plays a crucial role in understanding complex brain functions and driving advancements in artificial intelligence. This paper investigates the Mittag-Leffler projective synchronization in Caputo fractional-order memristive neural networks with reaction–diffusion dynamics and multiple time-varying delays. To address parameter mismatches and achieve synchronization, two adaptive controllers are designed: one for networks with bounded activation functions and another for those with unbounded functions. By leveraging fractional calculus, a novel inequality is derived for fractional-order systems with diverse time-varying delays. This inequality, combined with Green's formula, Fubini's theorem, and the Lyapunov functional method, leads to the establishment of algebraic conditions required for achieving Mittag-Leffler projective synchronization in these networks. Finally, numerical simulations validate the theoretical findings, demonstrating the efficacy and reliability of the proposed method.