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• W3089465544 abstract "With the help of Maple, the precise traveling wave solutions of three fractal-order model equations related to water waves, including hyperbolic solutions, trigonometric solutions, and rational solutions, are obtained by using function expansion method. An isolated wave solution is selected from the solution of each nonlinear dispersive wave model equation, and the influence of fractional order change on these isolated wave solutions is discussed. The results show that the fractional derivatives can modulate the waveform, local periodicity, and structure of the isolated solutions of the three model equations. We also point out the construction rules of the auxiliary equations of the extended (<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M1><mml:msup><mml:mrow><mml:mi>G</mml:mi></mml:mrow><mml:mrow><mml:mo>′</mml:mo></mml:mrow></mml:msup><mml:mo>/</mml:mo><mml:mi>G</mml:mi></mml:math>)-expansion method. In the “The Explanation and Discussion” section, a more generalized auxiliary equation is used to further emphasize the rules, which has certain reference value for the construction of the new auxiliary equations. The solutions of fractional-order nonlinear partial differential equations can be enriched by selecting other solvable equations as auxiliary equations." @default.
• W3089465544 created "2020-10-08" @default.
• W3089465544 creator A5007802647 @default.
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• W3089465544 date "2020-09-30" @default.
• W3089465544 modified "2023-09-25" @default.
• W3089465544 title "Mechanical Solving a Few Fractional Partial Differential Equations and Discussing the Effects of the Fractional Order" @default.
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• W3089465544 doi "https://doi.org/10.1155/2020/3758353" @default.
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