{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,6]],"date-time":"2026-04-06T21:00:20Z","timestamp":1775509220786,"version":"3.50.1"},"reference-count":45,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2023,1,20]],"date-time":"2023-01-20T00:00:00Z","timestamp":1674172800000},"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, the fractional\u2013space stochastic (2+1)-dimensional breaking soliton equation (SFSBSE) is taken into account in the sense of M-Truncated derivative. To get the exact solutions to the SFSBSE, we use the modified F-expansion method. There are several varieties of obtained exact solutions, including trigonometric and hyperbolic functions. The attained solutions of the SFSBSE established in this paper extend a number of previously attained results. Moreover, in order to clarify the influence of multiplicative noise and M-Truncated derivative on the behavior and symmetry of the solutions for the SFSBSE, we employ Matlab to plot three-dimensional and two-dimensional diagrams of the exact fractional\u2013stochastic solutions achieved here. In general, a noise term that destroy the symmetry of the solutions increases the solution\u2019s stability.<\/jats:p>","DOI":"10.3390\/sym15020288","type":"journal-article","created":{"date-parts":[[2023,1,20]],"date-time":"2023-01-20T02:43:29Z","timestamp":1674182609000},"page":"288","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":20,"title":["Effects of M-Truncated Derivative and Multiplicative Noise on the Exact Solutions of the Breaking Soliton Equation"],"prefix":"10.3390","volume":"15","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1402-7584","authenticated-orcid":false,"given":"Wael W.","family":"Mohammed","sequence":"first","affiliation":[{"name":"Department of Mathematics, Faculty of Science, University of Ha\u2019il, Ha\u2019il 81481, Saudi Arabia"},{"name":"Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7585-5519","authenticated-orcid":false,"given":"M.","family":"El-Morshedy","sequence":"additional","affiliation":[{"name":"Department of Mathematics, College of Science and Humanities in Al-Kharj, Prince Sattam bin Abdulaziz University, Al-Kharj 11942, Saudi Arabia"},{"name":"Department of Statistics and Computer Science, Faculty of Science, Mansoura University, Mansoura 35516, Egypt"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Abdelkader","family":"Moumen","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Science, University of Ha\u2019il, Ha\u2019il 81481, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ekram E.","family":"Ali","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Science, University of Ha\u2019il, Ha\u2019il 81481, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5639-6169","authenticated-orcid":false,"given":"M.","family":"Benaissa","sequence":"additional","affiliation":[{"name":"Chemical Engineering Department, College of Engineering, University of Ha\u2019il, Ha\u2019il 81441, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3363-7924","authenticated-orcid":false,"given":"Ahmed E.","family":"Abouelregal","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt"},{"name":"Department of Mathematics, College of Science and Arts, Jouf University, Sakakah 77455, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,1,20]]},"reference":[{"key":"ref_1","unstructured":"Oldham, K.B., and Spanier, J. 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