Mohammad S. Hijazi

This study addresses the problem of finite-time stability (FTS) for a discrete-time FitzHugh–Nagumo reaction–diffusion system (FHN–RDs) governed by a variable-order (VO) Caputo fractional difference operator. The discrete fractional formulation is obtained by combining a central difference approximation for the spatial derivative with a VO fractional operator for the temporal derivative. The analysis begins with proving the well-posedness of solutions for the proposed discrete model. The main contribution lies in establishing an FTS criterion. By employing a discrete fractional Gronwall-type inequality, we derive a sufficient stability condition expressed through the discrete Mittag–Leffler function (MLF). Finally, a numerical simulation is provided to illustrate the applicability of the theoretical findings, confirming that the system state remains bounded within a prescribed limit over a finite time horizon.

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.