This paper investigates the finite-time stability (FTS) of reaction-diffusion systems (RDs) governed by fractional-order (FO) dynamics, with a specific focus on the Selkov-Schnakenberg (SS) model. The study introduces theoretical stability conditions using Lyapunov function (LF)-based methods and Caputo fractional derivatives (CFD), providing a robust framework for analyzing equilibrium properties and synchronization in these systems. Numerical simulations validate the theoretical findings, demonstrating the system’s dynamic behavior under specified spatial and temporal conditions. The results highlight the influence of diffusion coefficients and reaction parameters on achieving FTS and underscore the practical applicability of the framework in modeling biological and chemical processes. This research contributes to the growing field of fractional-order systems, offering insights into their stability and synchronization within finite time frames.

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Finite-Time Stability Analysis of Reaction-Diffusion Systems with Fractional-Order Dynamics: A Study Using the Selkov-Schnakenberg Model

  • Issam Bendib,
  • Adel Ouannas,
  • Shaher Momani,
  • Chaouki Aouiti

摘要

This paper investigates the finite-time stability (FTS) of reaction-diffusion systems (RDs) governed by fractional-order (FO) dynamics, with a specific focus on the Selkov-Schnakenberg (SS) model. The study introduces theoretical stability conditions using Lyapunov function (LF)-based methods and Caputo fractional derivatives (CFD), providing a robust framework for analyzing equilibrium properties and synchronization in these systems. Numerical simulations validate the theoretical findings, demonstrating the system’s dynamic behavior under specified spatial and temporal conditions. The results highlight the influence of diffusion coefficients and reaction parameters on achieving FTS and underscore the practical applicability of the framework in modeling biological and chemical processes. This research contributes to the growing field of fractional-order systems, offering insights into their stability and synchronization within finite time frames.