This study aims to address the topic of finite-time synchronization within a specific subset of fractional-order Degn–Harrison reaction–diffusion systems. To achieve this goal, we begin with the introduction of a novel lemma specific for finite-time stability analysis. Diverging from existing criteria, this lemma represents a significant extension of prior findings, laying the groundwork for subsequent investigations. Building upon this foundation, we proceed to develop efficient dependent linear controllers designed to orchestrate finite-time synchronization. Leveraging the power of a Lyapunov function, we derive new, robust conditions that ensure the attainment of synchronization within a predefined time frame. This innovative approach not only enhances our understanding of finite-time synchronization, but also offers practical solutions for its realization in complex systems. To validate the efficacy and applicability of our proposed methodology, extensive numerical simulations are conducted. Through this comprehensive analysis, we aim to contribute valuable insights to the field of fractional-order reaction–diffusion systems while paving the way for practical implementations in real-world applications.

In this paper, we present an investigation into the stability of equilibrium points and synchronization within a finite time frame for fractional-order Lengyel–Epstein reaction-diffusion systems. Initially, we utilize Lyapunov theory and multiple criteria to examine the finite-time stability of equilibrium points. Following this analysis, we design efficient, interdependent linear controllers. By applying a Lyapunov function, we define new adequate conditions to ensure finite-time synchronization within a specified time interval. Finally, we provide two illustrative examples to demonstrate the effectiveness and practicality of our proposed method and validate the theoretical outcomes.

This paper investigates a fractional-order SEIR model to study the dynamics of infectious diseases, specifically COVID-19, by incorporating memory effects through fractional derivatives. The model’s formulation enhances the understanding of epidemic dynamics by considering disease transmission, recovery, and mortality rates under fractional calculus. Stability analyses are conducted for the disease-free equilibrium (DFE) and the pandemic fixed point (PFP), identifying critical conditions for finite-time stability using Lyapunov functions and fractional derivatives. Numerical simulations validate theoretical findings, demonstrating finitetime stabilization around the equilibrium points under realistic parameter settings. The results underscore the advantages of fractional-order modeling in capturing complex epidemic dynamics and highlight its potential to inform public health intervention strategies.

American scientific publishing group

American scientific publishing group