{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,11]],"date-time":"2026-05-11T23:32:33Z","timestamp":1778542353197,"version":"3.51.4"},"reference-count":39,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2024,3,8]],"date-time":"2024-03-08T00:00:00Z","timestamp":1709856000000},"content-version":"vor","delay-in-days":67,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100010272","name":"Zarqa University","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100010272","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Journal of Applied Mathematics"],"published-print":{"date-parts":[[2024,1]]},"abstract":"<jats:p>The KdV\u2010Burgers equation is one of the most important partial differential equations, established by Korteweg and de Vries to describe the behavior of nonlinear waves and many physical phenomena. In this paper, we reformulate this problem in the sense of Caputo fractional derivative, whose physical meanings, in this case, are very evident by describing the whole time domain of physical processing. The main aim of this work is to present the analytical approximate series for the nonlinear Caputo fractional KdV\u2010Burgers equation by applying the Laplace residual power series method. The main tools of this method are the Laplace transform, Laurent series, and residual function. Moreover, four attractive and satisfying applications are given and solved to elucidate the mechanism of our proposed method. The analytical approximate series solution via this sweet technique shows excellent agreement with the solution obtained from other methods in simple and understandable steps. Finally, graphical and numerical comparison results at different values of <jats:italic>\u03b1<\/jats:italic>\u2009 are provided with residual and relative errors to illustrate the behaviors of the approximate results and the effectiveness of the proposed method.<\/jats:p>","DOI":"10.1155\/2024\/7835548","type":"journal-article","created":{"date-parts":[[2024,3,9]],"date-time":"2024-03-09T00:52:26Z","timestamp":1709945546000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":10,"title":["Analytical Approximate Solutions of Caputo Fractional KdV\u2010Burgers Equations Using Laplace Residual Power Series Technique"],"prefix":"10.1155","volume":"2024","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1649-1073","authenticated-orcid":false,"given":"Aliaa","family":"Burqan","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5017-4082","authenticated-orcid":false,"given":"Mona","family":"Khandaqji","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8543-5497","authenticated-orcid":false,"given":"Zeyad","family":"Al-Zhour","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7470-8162","authenticated-orcid":false,"given":"Ahmad","family":"El-Ajou","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Tasneem","family":"Alrahamneh","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2024,3,8]]},"reference":[{"key":"e_1_2_10_1_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.cnsns.2018.04.019"},{"key":"e_1_2_10_2_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2019.03.008"},{"key":"e_1_2_10_3_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0304-0208(06)80001-0"},{"key":"e_1_2_10_4_2","doi-asserted-by":"publisher","DOI":"10.1155\/2022\/6939045"},{"key":"e_1_2_10_5_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.chaos.2020.109957"},{"key":"e_1_2_10_6_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.aej.2021.07.020"},{"key":"e_1_2_10_7_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.matcom.2021.02.021"},{"key":"e_1_2_10_8_2","doi-asserted-by":"publisher","DOI":"10.1140\/epjp\/s13360-020-01061-9"},{"key":"e_1_2_10_9_2","doi-asserted-by":"publisher","DOI":"10.3389\/fphy.2021.525250"},{"key":"e_1_2_10_10_2","doi-asserted-by":"publisher","DOI":"10.1007\/s40435-022-01020-5"},{"key":"e_1_2_10_11_2","doi-asserted-by":"publisher","DOI":"10.1007\/s40435-022-01001-8"},{"key":"e_1_2_10_12_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.aej.2022.04.004"},{"key":"e_1_2_10_13_2","doi-asserted-by":"publisher","DOI":"10.5391\/IJFIS.2022.22.1.23"},{"key":"e_1_2_10_14_2","doi-asserted-by":"publisher","DOI":"10.1080\/14786449508620739"},{"key":"e_1_2_10_15_2","doi-asserted-by":"publisher","DOI":"10.1063\/1.1664873"},{"key":"e_1_2_10_16_2","first-page":"602","article-title":"Operational matrices for solving Burgers equation by using block-pulse functions with error analysis","volume":"5","author":"Maleknejad K.","year":"2011","journal-title":"Australian Journal of Basic and Applied Sciences"},{"key":"e_1_2_10_17_2","first-page":"340","article-title":"New numerical approximations for space-time fractional Burgers\u2019 equations via a Legendre spectral-collocation method","volume":"67","author":"Bhrawy A. 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