{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,7]],"date-time":"2026-04-07T08:57:17Z","timestamp":1775552237971,"version":"3.50.1"},"reference-count":38,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2023,1,11]],"date-time":"2023-01-11T00:00:00Z","timestamp":1673395200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":["www.mdpi.com"],"crossmark-restriction":true},"short-container-title":["Symmetry"],"abstract":"<jats:p>Through the use of a unique approach, we study the fractional Biswas\u2013Milovic model with Kerr and parabolic law nonlinearities in this paper. The Caputo approach is used to take the fractional derivative. The method employed here is the homotopy perturbation transform method (HPTM), which combines the homotopy perturbation method (HPM) and Yang transform (YT). The HPTM combines the homotopy perturbation method, He\u2019s polynomials, and the Yang transform. He\u2019s polynomial is a wonderful tool for dealing with nonlinear terms. To confirm the validity of each result, the technique was substituted into the equation. The described techniques can be used to find the solutions to these kinds of equations as infinite series, and when these series are in closed form, they give a precise solution. Graphs are used to show the derived numerical results. The maple software package is used to carry out the numerical simulation work. The results of this research are highly positive and demonstrate how effective the suggested method is for mathematical modeling of natural occurrences.<\/jats:p>","DOI":"10.3390\/sym15010210","type":"journal-article","created":{"date-parts":[[2023,1,11]],"date-time":"2023-01-11T02:59:54Z","timestamp":1673405994000},"page":"210","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["On the Solution of Fractional Biswas\u2013Milovic Model via Analytical Method"],"prefix":"10.3390","volume":"15","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5210-8505","authenticated-orcid":false,"given":"Pongsakorn","family":"Sunthrayuth","sequence":"first","affiliation":[{"name":"Department of Mathematics and Computer Science, Faculty of Science and Technology, Rajamangala University of Technology Thanyaburi (RMUTT), Pathumthani 12110, Thailand"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4755-9381","authenticated-orcid":false,"given":"Muhammad","family":"Naeem","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Deanship of Applied Sciences, Umm Al-Qura University, Makkah 517, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1949-5643","authenticated-orcid":false,"given":"Nehad Ali","family":"Shah","sequence":"additional","affiliation":[{"name":"Department of Mechanical Engineering, Sejong University, Seoul 05006, Republic of Korea"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Rasool","family":"Shah","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Abdul Wali Khan University, Mardan 23200, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0862-0648","authenticated-orcid":false,"given":"Jae Dong","family":"Chung","sequence":"additional","affiliation":[{"name":"Department of Mechanical Engineering, Sejong University, Seoul 05006, Republic of Korea"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,1,11]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1140\/epjp\/i2019-12411-y","article-title":"A homotopy technique for a fractional order multi-dimensional telegraph equation via the Laplace transform","volume":"134","author":"Prakash","year":"2019","journal-title":"Eur. 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