Soliton solutions and fractional effects to the time-fractional modified equal width equation

The one-dimensional long water wave propagation in a nonlinear medium, including the dispersion process, is well simulated by the fractional-order modified equal-width (MEW) equation. This article establishes several recognized, standard, inclusive, and scores of typical exact wave solutions to the...

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Bibliographic Details
Published in:Alexandria engineering journal 2022-12, Vol.61 (12), p.12539-12547
Main Authors: Habibul Bashar, Md, Inc, Mustafa, Rayhanul Islam, S.M., Mahmoud, K.H., Ali Akbar, M.
Format: Article
Language:English
Subjects:
Analytical solutions
Conformable fractional derivative
Modified equal width equation
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Summary:The one-dimensional long water wave propagation in a nonlinear medium, including the dispersion process, is well simulated by the fractional-order modified equal-width (MEW) equation. This article establishes several recognized, standard, inclusive, and scores of typical exact wave solutions to the MEW equation using the double G'/G,1/G-expansion method. For specific parameter values, kink, periodic, periodic-singular, singular-kink, and other forms of solitons can be recovered from general solutions. The effect of the fractional parameter on wave forms has also been analyzed by depicting several graphs for different values of the fractional-order α. In order to illustrate the potential characteristics, three- and two-dimensional combined plots using Maple have been drawn. It has been established that the introduced approach is a potential tool for extracting new exact solutions to various nonlinear evolution equations (NLEEs) arising in engineering, science, and applied mathematics.
ISSN:1110-0168
DOI:10.1016/j.aej.2022.06.047