Mittag–Leffler synchronization of fractional‐order reaction–diffusion systems

Abstract This paper presents a rigorous analytical framework for investigating the Mittag–Leffler synchronization (MLSY) properties in fractional‐order reaction–diffusion systems (FO‐RDs). By incorporating a linear control strategy within a drive‐response configuration, we derive sufficient conditions under which the system states converge to their equilibrium point (EP). The analysis employs fractional calculus specifically Caputo fractional derivatives (CFDs) and Mittag–Leffler function estimates—in conjunction with Lyapunov function (LF) techniques to establish Mittag–Leffler stability (MLS) and synchronization despite the systems' inherent nonlinearities and spatial heterogeneity. The theoretical results are substantiated by numerical simulations on a glycolysis RD model, demonstrating rapid convergence and robust performance of the proposed control scheme. These findings underscore the potential applicability of the developed approach in diverse areas such as secure communications, biological system modeling, and complex network synchronization.