Mittag-Leffler Synchronization of Leakage and Time-Varying Delayed Complex-Valued Fractional-Order Memristor-Based Neural Networks

This paper investigates the global Mittag-Leffler (ML) synchronization problem for a class of complex-valued fractional-order memristor-based neural networks (CFMNNs) that are simultaneously subject to leakage delays and time-varying delays. By decomposing the complex-valued states and activation functions into their real and imaginary parts, and employing Filippov’s differential inclusion theory to handle the discontinuous memristive connection weights, we reformulate the original system into an equivalent real-valued framework. Two distinct control strategies—a state-feedback controller and an adaptive controller—are designed and rigorously analyzed. Using fractional-order Lyapunov functional methods together with suitable fractional inequalities, we derive explicit algebraic criteria that guarantee global ML synchronization. The adaptive controller offers enhanced flexibility because its gains are updated online and need not be prescribed in advance. A comparative simulation under identical parameters and initial conditions confirms that both control schemes synchronize the drive and response systems, and that the adaptive controller attains essentially the same fast convergence as the feedback scheme. Numerical examples are provided to illustrate the effectiveness and practicality of the obtained theoretical results, thereby filling a notable gap in the existing literature on synchronization of delayed fractional-order complex-valued memristive systems.