{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,16]],"date-time":"2026-04-16T03:31:45Z","timestamp":1776310305925,"version":"3.50.1"},"reference-count":38,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2024,9,11]],"date-time":"2024-09-11T00:00:00Z","timestamp":1726012800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Taif University, Saudi Arabia","award":["TU-DSPP-2024-289"],"award-info":[{"award-number":["TU-DSPP-2024-289"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Computation"],"abstract":"<jats:p>The fractional regularized long wave equation and the fractional nonlinear shallow-water wave equation are the noteworthy models in the domains of fluid dynamics, ocean engineering, plasma physics, and microtubules in living cells. In this study, a reliable and efficient improved F-expansion technique, along with the fractional beta derivative, has been utilized to explore novel soliton solutions to the stated wave equations. Consequently, the study establishes a variety of reliable and novel soliton solutions involving trigonometric, hyperbolic, rational, and algebraic functions. By setting appropriate values for the parameters, we obtained peakons, anti-peakon, kink, bell, anti-bell, singular periodic, and flat kink solitons. The physical behavior of these solitons is demonstrated in detail through three-dimensional, two-dimensional, and contour representations. The impact of the fractional-order derivative on the wave profile is notable and is illustrated through two-dimensional graphs. It can be stated that the newly established solutions might be further useful for the aforementioned domains.<\/jats:p>","DOI":"10.3390\/computation12090187","type":"journal-article","created":{"date-parts":[[2024,9,11]],"date-time":"2024-09-11T10:33:01Z","timestamp":1726050781000},"page":"187","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Exploring Soliton Solutions for Fractional Nonlinear Evolution Equations: A Focus on Regularized Long Wave and Shallow Water Wave Models with Beta Derivative"],"prefix":"10.3390","volume":"12","author":[{"given":"Sujoy","family":"Devnath","sequence":"first","affiliation":[{"name":"Department of Electrical and Electronic Engineering, Daffodil International University, Savar, Dhaka 1216, Bangladesh"}]},{"given":"Maha M.","family":"Helmi","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics, College of Science, Taif University, P.O. Box 11099, Taif 21944, Saudi Arabia"}]},{"given":"M. Ali","family":"Akbar","sequence":"additional","affiliation":[{"name":"Department of Applied Mathematics, University of Rajshahi, Rajshahi 6205, Bangladesh"}]}],"member":"1968","published-online":{"date-parts":[[2024,9,11]]},"reference":[{"key":"ref_1","unstructured":"Podlubny, I. (1998). 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