Exploring Soliton Solutions for Fractional Nonlinear Evolution Equations: A Focus on Regularized Long Wave and Shallow Water Wave Models with Beta Derivative

被引:1
作者
Devnath, Sujoy [1 ]
Helmi, Maha M. [2 ]
Akbar, M. Ali [3 ]
机构
[1] Daffodil Int Univ, Dept Elect & Elect Engn, Dhaka 1216, Bangladesh
[2] Taif Univ, Coll Sci, Dept Math & Stat, POB 11099, Taif 21944, Saudi Arabia
[3] Univ Rajshahi, Dept Appl Math, Rajshahi 6205, Bangladesh
关键词
improved F-expansion method; beta derivative; fractional regularized long wave equation; fractional nonlinear shallow-water wave equation; soliton solutions;
D O I
10.3390/computation12090187
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
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.
引用
收藏
页数:14
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