New Abundant Analytical Solitons to the Fractional Mathematical Physics Model via Three Distinct Schemes

Abdulrahman Alomair (), Abdulaziz S. Al Naim and Ahmet Bekir ()
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Abdulrahman Alomair: Accounting Department, Business School, King Faisal University, Al-Ahsa 31982, Saudi Arabia
Abdulaziz S. Al Naim: Accounting Department, Business School, King Faisal University, Al-Ahsa 31982, Saudi Arabia
Ahmet Bekir: Neighbourhood of Akcaglan, Imarli Street, Number: 28/4, 26030 Eskisehir, Turkey

Mathematics, 2024, vol. 12, issue 23, 1-24

Abstract: New types of truncated M-fractional wave solitons to the simplified Modified Camassa–Holm model, a mathematical physics model, are obtained. This model is used to explain the unidirectional propagation of shallow water waves. The required solutions are obtained by utilizing the simplest equation, the Sardar subequation, and the generalized Kudryashov schemes. The obtained results consist of the dark, singular, periodic, dark-bright, and many other analytical solitons. Dynamical behaviors of some obtained solutions are represented by two-dimensional (2D), three-dimensional (3D), and Contour graphs. An effect of fractional derivative is shown graphically. The results are newer than the existing results of the governing equation. Obtained solutions have much importance in the various areas of applied science as well as engineering. We concluded that the utilized methods are helpful and applicable for other partial fractional equations in applied science and engineering.

Keywords: fractional derivative; simplified modified Camassa–Holm model; analytical techniques; new M-fractional wave solutions (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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