{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T01:35:05Z","timestamp":1760232905692,"version":"build-2065373602"},"reference-count":46,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2022,12,8]],"date-time":"2022-12-08T00:00:00Z","timestamp":1670457600000},"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>In this article, we use the homotopy perturbation method and the Adomian decomposition method with the Yang transformation to discover analytical solution to the time-fractional coupled Schr\u00f6dinger\u2013KdV equation. In the Caputo sense, fractional derivatives are described. A convergent series is used to calculate the solutions of fractional PDEs. Analytical results achieved applying the homotopy perturbation and decomposition techniques are numerically calculated and represented in the form of tables and figures. The simplicity, efficacy, and high degree of accuracy of the used method are then demonstrated by comparing these solutions to the actual solutions and the results. Finally, the applied approaches are the most popular and convergent methods for solving nonlinear fractional-order partial deferential problems.<\/jats:p>","DOI":"10.3390\/sym14122602","type":"journal-article","created":{"date-parts":[[2022,12,9]],"date-time":"2022-12-09T02:20:31Z","timestamp":1670552431000},"page":"2602","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Analytical Approaches for Approximate Solution of the Time-Fractional Coupled Schr\u00f6dinger\u2013KdV Equation"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-4755-9381","authenticated-orcid":false,"given":"Muhammad","family":"Naeem","sequence":"first","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\/0000-0003-0199-6850","authenticated-orcid":false,"given":"Humaira","family":"Yasmin","sequence":"additional","affiliation":[{"name":"Department of Basic Sciences, Preparatory Year Deanship, King Faisal University, Al-Ahsa 31982, 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":"Jeevan","family":"Kafle","sequence":"additional","affiliation":[{"name":"Central Department of Mathematics, Tribhuvan University, Kirtipur 44618, Kathmandu, Nepal"}],"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":[[2022,12,8]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"4513","DOI":"10.1007\/s00500-020-05459-6","article-title":"W shaped surfaces to the nematic liquid crystals with three nonlinearity laws","volume":"25","author":"Ismael","year":"2021","journal-title":"Soft Comput."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"2715","DOI":"10.1016\/j.aej.2021.01.009","article-title":"The Schrodinger-KdV equation of fractional order with Mittag-Leffler nonsingular kernel","volume":"60","author":"Yavuz","year":"2021","journal-title":"Alex. 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