{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,6]],"date-time":"2026-05-06T22:40:30Z","timestamp":1778107230976,"version":"3.51.4"},"reference-count":37,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2022,10,11]],"date-time":"2022-10-11T00:00:00Z","timestamp":1665446400000},"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>Fractional\u2013stochastic Drinfel\u2019d\u2013Sokolov\u2013Wilson equations (FSDSWEs) forced by multiplicative Brownian motion are assumed. This equation is employed in mathematical physics, plasma physics, surface physics, applied sciences, and population dynamics. The (G\u2032\/G)-expansion method is utilized to find rational, hyperbolic, and trigonometric stochastic solutions for FSDSWEs. Because of the priority of FSDSWEs, the derived solutions are more useful and effective in understanding various important physical phenomena. Furthermore, we used the MATLAB package to create 3D graphs for specific solutions in order to investigate the effect of fractional-order and Brownian motions on the solutions of FSDSWEs.<\/jats:p>","DOI":"10.3390\/sym14102105","type":"journal-article","created":{"date-parts":[[2022,10,11]],"date-time":"2022-10-11T06:13:27Z","timestamp":1665468807000},"page":"2105","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":43,"title":["The Analytical Solutions of Stochastic-Fractional Drinfel\u2019d-Sokolov-Wilson Equations via (G\u2032\/G)-Expansion Method"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2394-0041","authenticated-orcid":false,"given":"Farah M.","family":"Al-Askar","sequence":"first","affiliation":[{"name":"Department of Mathematical Science, Collage of Science, Princess Nourah Bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1694-7907","authenticated-orcid":false,"given":"Clemente","family":"Cesarano","sequence":"additional","affiliation":[{"name":"Section of Mathematics, International Telematic University Uninettuno, Corso, Vittorio Emanuele II, 39, 00186 Rome, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1402-7584","authenticated-orcid":false,"given":"Wael W.","family":"Mohammed","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Collage of Science, University of Ha\u2019il, Ha\u2019il 2440, Saudi Arabia"},{"name":"Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,10,11]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"44","DOI":"10.1007\/s13324-021-00477-5","article-title":"A binary darboux transformation for multicomponent NLS equations and their reductions","volume":"11","author":"Ma","year":"2021","journal-title":"Anal. 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