{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,12]],"date-time":"2026-04-12T15:38:42Z","timestamp":1776008322566,"version":"3.50.1"},"reference-count":50,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2023,8,22]],"date-time":"2023-08-22T00:00:00Z","timestamp":1692662400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>The aim of this work is to describe the dynamics of a discrete fractional-order reaction\u2013diffusion FitzHugh\u2013Nagumo model. We established acceptable requirements for the local asymptotic stability of the system\u2019s unique equilibrium. Moreover, we employed a Lyapunov functional to show that the constant equilibrium solution is globally asymptotically stable. Furthermore, numerical simulations are shown to clarify and exemplify the theoretical results.<\/jats:p>","DOI":"10.3390\/axioms12090806","type":"journal-article","created":{"date-parts":[[2023,8,22]],"date-time":"2023-08-22T09:10:56Z","timestamp":1692695456000},"page":"806","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":34,"title":["The FitzHugh\u2013Nagumo Model Described by Fractional Difference Equations: Stability and Numerical Simulation"],"prefix":"10.3390","volume":"12","author":[{"given":"Tareq","family":"Hamadneh","sequence":"first","affiliation":[{"name":"Department of Mathematics, Faculty of Science, Al Zaytoonah University of Jordan, Amman 11733, Jordan"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6944-1689","authenticated-orcid":false,"given":"Amel","family":"Hioual","sequence":"additional","affiliation":[{"name":"Laboratory of Dynamical Systems and Control, University of Oum EL-Bouaghi, Oum El Bouaghi 04000, Algeria"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3765-5807","authenticated-orcid":false,"given":"Omar","family":"Alsayyed","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Science, The Hashemite University, P.O. Box 330127, Zarqa 13133, Jordan"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8683-6698","authenticated-orcid":false,"given":"Yazan Alaya","family":"Al-Khassawneh","sequence":"additional","affiliation":[{"name":"Data Science and Artificial Intelligence Department, Zarqa University, Zarqa 13110, Jordan"}]},{"given":"Abdallah","family":"Al-Husban","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Science and Technology, Irbid National University, Irbid 21110, Jordan"}]},{"given":"Adel","family":"Ouannas","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Computer Science, University of Oum EL-Bouaghi, Oum El Bouaghi 04000, Algeria"}]}],"member":"1968","published-online":{"date-parts":[[2023,8,22]]},"reference":[{"key":"ref_1","unstructured":"Miller, K.S., and Ross, B. (1993). An Introduction to the Fractional Calculus and Fractional Differential Equations, Wiley."},{"key":"ref_2","unstructured":"Spanier, J. (1974). 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