The FitzHugh–Nagumo Model Described by Fractional Difference Equations: Stability and Numerical Simulation

Hamadneh, Tareq; Hioual, Amel; Alsayyed, Omar; Al-Khassawneh, Yazan Alaya; Al-Husban, Abdallah; Ouannas, Adel

doi:10.3390/axioms12090806

Cited by 9 publications

(1 citation statement)

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“…These efforts together enhance our grasp of the interaction between fractional dynamics and diffusion phenomena. For a more comprehensive exploration into the dynamics of fractional discrete reaction-diffusion models, one can find additional insights in [31][32][33].…”

Section: Introductionmentioning

confidence: 99%

On Stability of a Fractional Discrete Reaction–Diffusion Epidemic Model

Alsayyed,

Hioual,

Gharib

et al. 2023

Fractal Fract

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This paper considers the dynamical properties of a space and time discrete fractional reaction–diffusion epidemic model, introducing a novel generalized incidence rate. The linear stability of the equilibrium solutions of the considered discrete fractional reaction–diffusion model has been carried out, and a global asymptotic stability analysis has been undertaken. We conducted a global stability analysis using a specialized Lyapunov function that captures the system’s historical data, distinguishing it from the integer-order version. This approach significantly advanced our comprehension of the complex stability properties within discrete fractional reaction–diffusion epidemic models. To substantiate the theoretical underpinnings, this paper is accompanied by numerical examples. These examples serve a dual purpose: not only do they validate the theoretical findings, but they also provide illustrations of the practical implications of the proposed discrete fractional system.

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Section: Introductionmentioning

confidence: 99%