{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,13]],"date-time":"2026-04-13T20:14:59Z","timestamp":1776111299514,"version":"3.50.1"},"reference-count":60,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2023,1,12]],"date-time":"2023-01-12T00:00:00Z","timestamp":1673481600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>The main goal of the current work is to develop numerical approaches that use the Yang transform, the homotopy perturbation method (HPM), and the Adomian decomposition method to analyze the fractional model of the regularized long-wave equation. The shallow-water waves and ion-acoustic waves in plasma are both explained by the regularized long-wave equation. The first method combines the Yang transform with the homotopy perturbation method and He\u2019s polynomials. In contrast, the second method combines the Yang transform with the Adomian polynomials and the decomposition method. The Caputo sense is applied to the fractional derivatives. The strategy\u2019s effectiveness is shown by providing a variety of fractional and integer-order graphs and tables. To confirm the validity of each result, the technique was substituted into the equation. The described methods 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 the precise solution. The results support the claim that this approach is simple, strong, and efficient for obtaining exact solutions for nonlinear fractional differential equations. The method is a strong contender to contribute to the existing literature.<\/jats:p>","DOI":"10.3390\/sym15010220","type":"journal-article","created":{"date-parts":[[2023,1,12]],"date-time":"2023-01-12T06:25:57Z","timestamp":1673504757000},"page":"220","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":22,"title":["Investigation of Fractional Nonlinear Regularized Long-Wave Models via Novel Techniques"],"prefix":"10.3390","volume":"15","author":[{"given":"Muhammad","family":"Naeem","sequence":"first","affiliation":[{"name":"Department of Mathematics, Umm Al-Qura University, Makkah 517, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0199-6850","authenticated-orcid":false,"given":"Humaira","family":"Yasmin","sequence":"additional","affiliation":[{"name":"Department of Basic Sciences, King Faisal University, Al-Ahsa 31982, Saudi Arabia"}],"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\/0000-0002-1949-5643","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"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7469-5402","authenticated-orcid":false,"given":"Kamsing","family":"Nonlaopon","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen 40002, Thailand"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,1,12]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"717","DOI":"10.1007\/BF02457746","article-title":"Numerical research on the coherent structure in the viscoelastic second-order mixing layers","volume":"19","author":"Zhaosheng","year":"1998","journal-title":"Appl. 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