{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,7]],"date-time":"2026-04-07T04:51:26Z","timestamp":1775537486253,"version":"3.50.1"},"reference-count":31,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2023,4,30]],"date-time":"2023-04-30T00:00:00Z","timestamp":1682812800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>In the current study, we investigate the stochastic Benjamin\u2013Bona\u2013Mahony equation with beta derivative (SBBME-BD). The considered stochastic term is the multiplicative noise in the It\u00f4 sense. By combining the F-expansion approach with two separate equations, such as the Riccati and elliptic equations, new hyperbolic, trigonometric, rational, and Jacobi elliptic solutions for SBBME-BD can be generated. The solutions to the Benjamin\u2013Bona\u2013Mahony equation are useful in understanding various scientific phenomena, including Rossby waves in spinning fluids and drift waves in plasma. Our results are presented using MATLAB, with numerous 3D and 2D figures illustrating the impacts of white noise and the beta derivative on the obtained solutions of SBBME-BD.<\/jats:p>","DOI":"10.3390\/axioms12050447","type":"journal-article","created":{"date-parts":[[2023,5,1]],"date-time":"2023-05-01T12:12:11Z","timestamp":1682943131000},"page":"447","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":13,"title":["The Influence of White Noise and the Beta Derivative on the Solutions of the BBM Equation"],"prefix":"10.3390","volume":"12","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 Roma, 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":[[2023,4,30]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"12085","DOI":"10.1016\/j.ijleo.2016.09.116","article-title":"Exact solitary wave solutions to the generalized Fisher equation","volume":"127","author":"Zhou","year":"2016","journal-title":"Optik"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"105615","DOI":"10.1016\/j.rinp.2022.105615","article-title":"The solution of fractional-order system of KdV equations with exponential-decay kernel","volume":"38","author":"Alshammari","year":"2022","journal-title":"Results Phys."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"52","DOI":"10.1080\/17455030.2014.956847","article-title":"Optical solitons in medium with parabolic law nonlinearity and higher order dispersion","volume":"25","author":"Zhou","year":"2015","journal-title":"Waves Random Complex Media"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"613","DOI":"10.1080\/17455030.2016.1181811","article-title":"New wave behaviors of the system of equations for the ion sound and Langmuir","volume":"26","author":"Baskonus","year":"2016","journal-title":"Waves Waves Random Complex Media"},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Al-Askar, F.M., Mohammed, W.W., Albalahi, A.M., and El-Morshedy, M. 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