{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,19]],"date-time":"2026-02-19T22:21:16Z","timestamp":1771539676668,"version":"3.50.1"},"reference-count":35,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2022,11,30]],"date-time":"2022-11-30T00:00:00Z","timestamp":1669766400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Basque Government","award":["IT1155-22"],"award-info":[{"award-number":["IT1155-22"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>This article presents an idea of a new approach for the solitary wave solution of the modified Degasperis\u2013Procesi (mDP) and modified Camassa\u2013Holm (mCH) models with a time-fractional derivative. We combine Laplace transform (LT) and homotopy perturbation method (HPM) to formulate the idea of the Laplace transform homotopy perturbation method (LHPTM). This study is considered under the Caputo sense. This proposed strategy does not depend on any assumption and restriction of variables, such as in the classical perturbation method. Some numerical examples are demonstrated and their results are compared graphically in 2D and 3D distribution. This approach presents the iterations in the form of a series solutions. We also compute the absolute error to show the effective performance of this proposed scheme.<\/jats:p>","DOI":"10.3390\/sym14122532","type":"journal-article","created":{"date-parts":[[2022,11,30]],"date-time":"2022-11-30T04:32:53Z","timestamp":1669782773000},"page":"2532","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["A Computational Scheme for the Numerical Results of Time-Fractional Degasperis\u2013Procesi and Camassa\u2013Holm Models"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9349-4729","authenticated-orcid":false,"given":"Muhammad","family":"Nadeem","sequence":"first","affiliation":[{"name":"School of Mathematics and Statistics, Qujing Normal University, Qujing 655011, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6807-6675","authenticated-orcid":false,"given":"Hossein","family":"Jafari","sequence":"additional","affiliation":[{"name":"Department of Mathematical Sciences, University of South Africa, UNISA, Pretoria 0003, South Africa"},{"name":"Department of Mathematics and Informatics, Azerbaijan University, Jeyhun Hajibeyli, 71, AZ1007 Baku, Azerbaijan"},{"name":"Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 110122, Taiwan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9832-1424","authenticated-orcid":false,"given":"Ali","family":"Akg\u00fcl","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Art and Science Faculty, Siirt University, 56100 Siirt, Turkey"},{"name":"Department of Mathematics, Mathematics Research Center, Near East University, Near East Boulevard, Mersin 10, 99138 Nicosia, Turkey"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9320-9433","authenticated-orcid":false,"given":"Manuel","family":"De la Sen","sequence":"additional","affiliation":[{"name":"Department of Electricity and Electronics, Institute of Research and Development of Processes, Faculty of Science and Technology, University of the Basque Country, 48940 Leioa, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,11,30]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Akdemir, A.O., Butt, S.I., Nadeem, M., and Ragusa, M.A. (2021). 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