{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,20]],"date-time":"2026-02-20T16:01:02Z","timestamp":1771603262466,"version":"3.50.1"},"reference-count":31,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2023,3,20]],"date-time":"2023-03-20T00:00:00Z","timestamp":1679270400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001871","name":"The Portuguese Foundation for Science and Technology (FCT\u2014Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia)","doi-asserted-by":"publisher","award":["UIDB\/50008\/2020"],"award-info":[{"award-number":["UIDB\/50008\/2020"]}],"id":[{"id":"10.13039\/501100001871","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001871","name":"The Portuguese Foundation for Science and Technology (FCT\u2014Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia)","doi-asserted-by":"publisher","award":["UIDB\/04106\/2020"],"award-info":[{"award-number":["UIDB\/04106\/2020"]}],"id":[{"id":"10.13039\/501100001871","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Mathematics"],"abstract":"<jats:p>In this article, we develop a simple mathematical GNU Octave\/MATLAB code that is easy to modify for the simulation of mathematical models governed by fractional-order differential equations, and for the resolution of fractional-order optimal control problems through Pontryagin\u2019s maximum principle (indirect approach to optimal control). For this purpose, a fractional-order model for the respiratory syncytial virus (RSV) infection is considered. The model is an improvement of one first proposed by the authors in 2018. The initial value problem associated with the RSV infection fractional model is numerically solved using Garrapa\u2019s fde12 solver and two simple methods coded here in Octave\/MATLAB: the fractional forward Euler\u2019s method and the predict-evaluate-correct-evaluate (PECE) method of Adams\u2013Bashforth\u2013Moulton. A fractional optimal control problem is then formulated having treatment as the control. The fractional Pontryagin maximum principle is used to characterize the fractional optimal control and the extremals of the problem are determined numerically through the implementation of the forward-backward PECE method. The implemented algorithms are available on GitHub and, at the end of the paper, in appendixes, both for the uncontrolled initial value problem as well as for the fractional optimal control problem, using the free GNU Octave computing software and assuring compatibility with MATLAB.<\/jats:p>","DOI":"10.3390\/math11061511","type":"journal-article","created":{"date-parts":[[2023,3,21]],"date-time":"2023-03-21T02:36:22Z","timestamp":1679366182000},"page":"1511","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":22,"title":["Numerical Fractional Optimal Control of Respiratory Syncytial Virus Infection in Octave\/MATLAB"],"prefix":"10.3390","volume":"11","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5153-4879","authenticated-orcid":false,"given":"Silv\u00e9rio","family":"Rosa","sequence":"first","affiliation":[{"name":"Department of Mathematics, Instituto de Telecomunica\u00e7\u00f5es, University of Beira Interior, 6201-001 Covilh\u00e3, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8641-2505","authenticated-orcid":false,"given":"Delfim F. M.","family":"Torres","sequence":"additional","affiliation":[{"name":"Center for Research and Development in Mathematics and Applications (CIDMA), Department of Mathematics, University of Aveiro, 3810-193 Aveiro, Portugal"}]}],"member":"1968","published-online":{"date-parts":[[2023,3,20]]},"reference":[{"key":"ref_1","first-page":"301","article-title":"Letter from Hanover, Germany to GFA L\u2019Hospital, September 30, 1695","volume":"2","author":"Leibniz","year":"1849","journal-title":"Math. Schriften"},{"key":"ref_2","first-page":"xxiv+340","article-title":"An introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications","volume":"Volume 198","author":"Podlubny","year":"1999","journal-title":"Mathematics in Science and Engineering"},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Rezapour, S., Etemad, S., Agarwal, R.P., and Nonlaopon, K. (2022). 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