{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T01:37:33Z","timestamp":1760060253322,"version":"build-2065373602"},"reference-count":37,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2025,8,10]],"date-time":"2025-08-10T00:00:00Z","timestamp":1754784000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"King Khalid University","award":["RGP 2\/248\/46"],"award-info":[{"award-number":["RGP 2\/248\/46"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>This study focuses on analyzing the generalized HSC-KdV equations characterized by variable coefficients and Wick-type stochastic (Wt.S) elements. To derive white noise functional (WNF) solutions, we employ the Hermite transform, the homogeneous balance principle, and the Fe (F-expansion) technique. Leveraging the inherent connection between hypercomplex system (HCS) theory and white noise (WN) analysis, we establish a comprehensive framework for exploring stochastic partial differential equations (PDEs) involving non-Gaussian parameters (N-GP). As a result, exact solutions expressed through Jacobi elliptic functions (JEFs) and trigonometric and hyperbolic forms are obtained for both the variable coefficients and stochastic forms of the generalized HSC-KdV equations. An illustrative example is included to validate the theoretical findings.<\/jats:p>","DOI":"10.3390\/axioms14080624","type":"journal-article","created":{"date-parts":[[2025,8,11]],"date-time":"2025-08-11T09:59:13Z","timestamp":1754906353000},"page":"624","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Analytical Solutions for Generalized Stochastic HSC-KdV Equations with Variable Coefficients Using Hermite Transform and F-Expansion Method"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-4312-8330","authenticated-orcid":false,"given":"Mohammed","family":"Zakarya","sequence":"first","affiliation":[{"name":"Department of Mathematics, College of Science, King Khalid University, P.O. Box 9004, Abha 61413, Saudi Arabia"}]},{"given":"Nadiah Zafer","family":"Al-Shehri","sequence":"additional","affiliation":[{"name":"Department of Mathematics, College of Science, King Khalid University, P.O. Box 9004, Abha 61413, Saudi Arabia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0159-6726","authenticated-orcid":false,"given":"Hegagi M.","family":"Ali","sequence":"additional","affiliation":[{"name":"Department of Mathematics, College of Science, University of Bisha, Bisha 61922, Saudi Arabia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5063-5301","authenticated-orcid":false,"given":"Mahmoud A.","family":"Abd-Rabo","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Science, Al-Azhar University, Assiut 71524, Egypt"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6782-7908","authenticated-orcid":false,"given":"Haytham M.","family":"Rezk","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Science, Al-Azhar University, Nasr City 11884, Egypt"}]}],"member":"1968","published-online":{"date-parts":[[2025,8,10]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"215","DOI":"10.1016\/0034-4877(96)83621-4","article-title":"A connection between the theory of hypergroups and white noise analysis","volume":"36","author":"Berezansky","year":"1995","journal-title":"Rep. 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