{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,28]],"date-time":"2025-11-28T12:39:13Z","timestamp":1764333553044,"version":"build-2065373602"},"reference-count":35,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2025,7,1]],"date-time":"2025-07-01T00:00:00Z","timestamp":1751328000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>This study applies the Conformable Laplace Adomian Decomposition Method (CLADM) to solve generalized time-fractional Korteweg\u2013de Vries (KdV) models, including seventh- and fifth-order models. CLADM combines the conformable fractional derivative and Laplace transform with the Adomian decomposition technique, offering analytic approximate solutions. Numerical and graphical results, generated using MATLAB R2020a 9.8.0.1323502, validate the method\u2019s efficiency and precision in capturing fractional-order dynamics. Fractional parameters \u03f1 significantly influence wave behavior, with higher orders yielding smoother profiles and reduced oscillations. Comparative analysis confirms CLADM\u2019s superiority over existing methods in minimizing errors. The versatility of CLADM highlights its potential for studying nonlinear wave phenomena in diverse applications.<\/jats:p>","DOI":"10.3390\/axioms14070511","type":"journal-article","created":{"date-parts":[[2025,7,1]],"date-time":"2025-07-01T06:56:54Z","timestamp":1751353014000},"page":"511","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["A Novel Computational Framework for Time-Fractional Higher-Order KdV Models: CLADM-Based Solutions and Comparative Analysis"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-8139-7545","authenticated-orcid":false,"given":"Priti V.","family":"Tandel","sequence":"first","affiliation":[{"name":"Department of Mathematics, Veer Narmad South Gujarat University, Surat 395007, Gujarat, India"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2104-2934","authenticated-orcid":false,"given":"Anant","family":"Patel","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Veer Narmad South Gujarat University, Surat 395007, Gujarat, India"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5979-160X","authenticated-orcid":false,"given":"Trushitkumar","family":"Patel","sequence":"additional","affiliation":[{"name":"Department of General Studies, University of the People, Pasadena, CA 91101, USA"}]}],"member":"1968","published-online":{"date-parts":[[2025,7,1]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.aej.2023.02.007","article-title":"Traveling wave solutions of generalized seventh-order time-fractional kdv models through he-laplace algorithm","volume":"70","author":"Qayyum","year":"2023","journal-title":"Alex. 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