{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,12]],"date-time":"2026-04-12T15:34:39Z","timestamp":1776008079028,"version":"3.50.1"},"reference-count":35,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2023,7,27]],"date-time":"2023-07-27T00:00:00Z","timestamp":1690416000000},"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>Discrete fractional models with reaction-diffusion have gained significance in the scientific field in recent years, not only due to the need for numerical simulation but also due to the stated biological processes. In this paper, we investigate the problem of synchronization-control in a fractional discrete nonlinear bacterial culture reaction-diffusion model using the Caputo h-difference operator and a second-order central difference scheme and an L1 finite difference scheme after deriving the discrete fractional version of the well-known Degn\u2013Harrison system and Lengyel\u2013Epstein system. Using appropriate techniques and the direct Lyapunov method, the conditions for full synchronization are determined.Furthermore, this research shows that the L1 finite difference scheme and the second-order central difference scheme may successfully retain the properties of the related continuous system. The conclusions are proven throughout the paper using two major biological models, and numerical simulations are carried out to demonstrate the practical use of the recommended technique.<\/jats:p>","DOI":"10.3390\/axioms12080728","type":"journal-article","created":{"date-parts":[[2023,7,27]],"date-time":"2023-07-27T02:14:48Z","timestamp":1690424088000},"page":"728","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":24,"title":["Synchronization of Fractional Partial Difference Equations via Linear Methods"],"prefix":"10.3390","volume":"12","author":[{"given":"Ibraheem","family":"Abu Falahah","sequence":"first","affiliation":[{"name":"Department of Mathematics, Faculty of Science, The Hashemite University, P.O. Box 330127, Zarqa 13133, 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 Larbi Ben M\u2019hidi, Oum El Bouaghi 04000, Algeria"}]},{"given":"Mowafaq Omar","family":"Al-Qadri","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Jerash University, Jerash 26150, 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 2600, Jordan"}]},{"given":"Tareq","family":"Hamadneh","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Science, Al Zaytoonah University of Jordan, Amman 11733, Jordan"}]},{"given":"Adel","family":"Ouannas","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Computer Science, University of Larbi Ben M\u2019hidi, Oum El Bouaghi 04000, Algeria"}]}],"member":"1968","published-online":{"date-parts":[[2023,7,27]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"91829","DOI":"10.1109\/ACCESS.2020.2993784","article-title":"Synchronization methods for the Degn-Harrison reaction-diffusion systems","volume":"8","author":"Mesdoui","year":"2020","journal-title":"IEEE Access"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"2832781","DOI":"10.1155\/2019\/2832781","article-title":"Synchronization control in reaction-diffusion systems: Application to Lengyel-Epstein system","volume":"2019","author":"Ouannas","year":"2019","journal-title":"Complexity"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"934","DOI":"10.1016\/j.camwa.2012.01.056","article-title":"Synchronization and control of coupled reaction\u2013diffusion systems of the FitzHugh\u2013Nagumo type","volume":"64","author":"Ambrosio","year":"2012","journal-title":"Comput. 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