{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T01:28:25Z","timestamp":1760232505173,"version":"build-2065373602"},"reference-count":29,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2022,11,4]],"date-time":"2022-11-04T00:00:00Z","timestamp":1667520000000},"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 KdV equation has many applications in mechanics and wave dynamics. Therefore, researchers are carrying out work to develop and analyze modified and generalized forms of the standard KdV equation. In this paper, we inspect the KdV-mKdV equation, which is a modified and generalized form of the ordinary KdV equation. We use the fractional operator in the Caputo sense to analyze the equation. We examine some theoretical results concerned with the solution\u2019s existence, uniqueness, and stability. We employ a modified Laplace method to extract the numerical results of the considered equation. We use MATLAB-2020 to simulate the results in a few fractional orders. We report the effects of the fractional order on the wave dynamics of the proposed equation.<\/jats:p>","DOI":"10.3390\/sym14112316","type":"journal-article","created":{"date-parts":[[2022,11,4]],"date-time":"2022-11-04T04:00:51Z","timestamp":1667534451000},"page":"2316","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Analysis of Kink Behaviour of KdV-mKdV Equation under Caputo Fractional Operator with Non-Singular Kernel"],"prefix":"10.3390","volume":"14","author":[{"given":"Sajjad","family":"Ali","sequence":"first","affiliation":[{"name":"Department of Mathematics, University of Malakand, Chakdara 18800, Khyber Pakhtunkhwa, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Aman","family":"Ullah","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of Malakand, Chakdara 18800, Khyber Pakhtunkhwa, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5610-6248","authenticated-orcid":false,"given":"Shabir","family":"Ahmad","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of Malakand, Chakdara 18800, Khyber Pakhtunkhwa, Pakistan"}],"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"}]},{"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":"Mathematics Research Center, Department of Mathematics, Near East University, Near East Boulevard, 99138 Nicosia, Turkey"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,11,4]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Wazwaz, A.M. 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