On new analytical solutions of fractional systems in shallow water dynamics

Authors

DOI:

https://doi.org/10.31349/RevMexFis.68.050701

Keywords:

Nonlinear fractional partial differential equation, shallow water waves, analytical wave solution, conformable fractional derivative

Abstract

Recently, fractional calculus has got considerable attention from researchers since many problems in natural sciences and engineering are modelled with differential equations having fractional order. The nonlinear coupled time-fractional Boussinesq-Burger (B-B) equation, the nonlinear time-fractional long water wave (ALW) equation, and the nonlinear (2+1)-dimensional space-time fractional generalized Nizhnik-Novikov-Veselov (GNNV) equation are used to express the structure of shallow water waves (SWWs) with different distributions. The analytical solutions of these equations play a substantial role in explaining the properties of complex phenomena in applied sciences. In the current work, we utilize the exponential rational function (ERF) method with the definition of fractional derivative in the conformable sense to achieve new exact traveling wave solutions of these fractional systems. The correctness, validity, and graphics of the new traveling wave solutions are achieved with the aid of Mathematica. Results demonstrate the effectiveness and strength of this technique to solve the system of fractional differential equations (FDEs).

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Published

2022-08-16

How to Cite

[1]
G. Bakıcıerler and E. Mısırlı, “On new analytical solutions of fractional systems in shallow water dynamics”, Rev. Mex. Fís., vol. 68, no. 5 Sep-Oct, pp. 050701 1–, Aug. 2022.

Issue

Vol. 68 No. 5 Sep-Oct (2022): Revista Mexicana de Física

Section

07 Gravitation, Mathematical Physics and Field Theory

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Copyright (c) 2022 Gizel Bakıcıerler, Emine Mısırlı

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