A Novel Analytical Framework for Investigating Mittag—Leffler Stability in Fractional Order Reaction—Diffusion Systems

Abstract

In this paper, we develop a novel analytical framework to investigate the Mittag-Leffler stability (MLS) of fractional order reaction—diffusion systems (FO-RDs). By employing fractional calculus and Lyapunov function (LF) techniques, we derive sufficient conditions that guarantee the system’s equilibrium point (EP) is reached within a settling time (ST). Our approach provides explicit estimates for the ST, linking the fractional dynamics to practical stability criteria. The theoretical results are rigorously validated through numerical simulations on a glycolysis RD model, which demonstrates rapid convergence of the state trajectories to the unique equilibrium. These findings not only deepen the understanding of the transient behavior in FO-RDs but also pave the way for applications in biomedical engineering, chemical reactor design, and environmental management, where swift stabilization is essential.OPEN ACCESS Received: 30/03/2025 Accepted: 17/06/2025 Published: 22/09/202