Control Strategies for Mittag-Leffler Synchronization in Variable-Order Fractional FitzHugh-Nagumo Reaction-Diffusion Networks

Abstract

This work presents a synchronization control methodology for Variable Fractional-Order Reaction-Diffusion systems (VFO-RDs), focusing on the FitzHugh-Nagumo model. Using Caputo fractional difference operators with time-dependent orders, we design both linear and nonlinear controllers and prove Mittag-Leffler synchronization under explicit constraints. Key contributions: (i) a unified Mittag-Leffler Synchronization (MLSY) framework for variableorder systems using linear and nonlinear controllers; (ii) integration of absolute-state feedback with Lyapunov-based stability for robustness and fast convergence; (iii) demonstration on the FitzHugh-Nagumo (FHN) model, indicating broader applicability in neural engineering.