{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,23]],"date-time":"2026-06-23T22:48:50Z","timestamp":1782254930931,"version":"3.54.5"},"reference-count":24,"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\/"}],"funder":[{"name":"National Council of Science and Technology of Mexico (CONACYT)","award":["A1-S-45928"],"award-info":[{"award-number":["A1-S-45928"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>In this study, we provide an efficient simulation to investigate the behavior of the solution to the Brusselator system (a biodynamic system) with the Rabotnov fractional-exponential (RFE) kernel fractional derivative. A system of fractional differential equations can be used to represent this model. The fractional-order derivative of a polynomial function tp is approximated in terms of the RFE kernel. In this work, we employ shifted Vieta\u2013Lucas polynomials in the spectral collocation technique. This process transforms the mathematical model into a set of algebraic equations. By assessing the residual error function, we can confirm that the provided approach is accurate and efficient. The outcomes demonstrate the effectiveness and simplicity of the technique for accurately simulating such models.<\/jats:p>","DOI":"10.3390\/sym15091619","type":"journal-article","created":{"date-parts":[[2023,8,22]],"date-time":"2023-08-22T08:58:54Z","timestamp":1692694734000},"page":"1619","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":13,"title":["Vieta\u2013Lucas Polynomials for the Brusselator System with the Rabotnov Fractional-Exponential Kernel Fractional Derivative"],"prefix":"10.3390","volume":"15","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3844-139X","authenticated-orcid":false,"given":"Mohamed M.","family":"Khader","sequence":"first","affiliation":[{"name":"Department of Mathematics and Statistics, College of Science, Imam Mohammad, Ibn Saud Islamic University (IMSIU), Riyadh 11566, Saudi Arabia"},{"name":"Department of Mathematics, Faculty of Science, Benha University, Benha 13511, Egypt"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7580-7533","authenticated-orcid":false,"given":"Jorge E.","family":"Mac\u00edas-D\u00edaz","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Didactics of Mathematics, Tallinn University, 10120 Tallinn, Estonia"},{"name":"Departamento de Matem\u00e1ticas y F\u00edsica, Universidad Aut\u00f3noma de Aguascalientes, Aguascalientes 20100, Mexico"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6381-6806","authenticated-orcid":false,"given":"Khaled M.","family":"Saad","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Arts and Sciences, Najran University, Najran 66445, Saudi Arabia"},{"name":"Department of Mathematics, Faculty of Applied Science, Taiz University, Taiz 6803, Yemen"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5911-7364","authenticated-orcid":false,"given":"Waleed M.","family":"Hamanah","sequence":"additional","affiliation":[{"name":"Interdisciplinary Research Center for Renewable Energy and Power Systems, King Fahd University for Petroleum and Minerals, Dhahran 31261, Saudi Arabia"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2023,8,22]]},"reference":[{"key":"ref_1","unstructured":"Kilbas, S.G., Kilbas, A.A., and Marichev, O.I. 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