Fractional transformation method for constructing solitary wave solutions to some nonlinear fractional partial differential equations

2014 ◽  
Vol 8 ◽  
pp. 5751-5762 ◽  
Author(s):  
Safwan Al-Shara'
Keyword(s):  
Partial Differential Equations ◽  
Solitary Wave ◽  
Differential Equations ◽  
Transformation Method ◽  
Solitary Wave Solutions ◽  
Fractional Partial Differential Equations ◽  
Partial Differential ◽  
Wave Solutions

scholarly journals Some Applications of the (G′/G,1/G)-Expansion Method for Finding Exact Traveling Wave Solutions of Nonlinear Fractional Evolution Equations

Symmetry ◽  
2019 ◽  
Vol 11 (8) ◽  
pp. 952
Author(s):  
Sekson Sirisubtawee ◽  
Sanoe Koonprasert ◽  
Surattana Sungnul
Keyword(s):  
Partial Differential Equations ◽  
Solitary Wave ◽  
Differential Equations ◽  
Exact Solutions ◽  
Traveling Wave ◽  
Expansion Method ◽  
Hyperbolic Function ◽  
Solitary Wave Solutions ◽  
Partial Differential ◽  
Wave Solutions

In this paper, the ( G ′ / G , 1 / G ) -expansion method is applied to acquire some new, exact solutions of certain interesting, nonlinear, fractional-order partial differential equations arising in mathematical physics. The considered equations comprise the time-fractional, (2+1)-dimensional extended quantum Zakharov-Kuznetsov equation, and the space-time-fractional generalized Hirota-Satsuma coupled Korteweg-de Vries (KdV) system in the sense of the conformable fractional derivative. Applying traveling wave transformations to the equations, we obtain the corresponding ordinary differential equations in which each of them provides a system of nonlinear algebraic equations when the method is used. As a result, many analytical exact solutions obtained of these equations are expressed in terms of hyperbolic function solutions, trigonometric function solutions, and rational function solutions. The graphical representations of some obtained solutions are demonstrated to better understand their physical features, including bell-shaped solitary wave solutions, singular soliton solutions, solitary wave solutions of kink type, and so on. The method is very efficient, powerful, and reliable for solving the proposed equations and other nonlinear fractional partial differential equations with the aid of a symbolic software package.

Analytical new soliton wave solutions of the nonlinear conformable time-fractional coupled Whitham–Broer–Kaup equations

2021 ◽  
pp. 2150492
Author(s):  
Delmar Sherriffe ◽  
Diptiranjan Behera ◽  
P. Nagarani
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Fractional Derivative ◽  
Function Method ◽  
Visual Representations ◽  
Fractional Partial Differential Equations ◽  
Partial Differential ◽  
Varying Parameters ◽  
Wave Solutions ◽  
Soliton Wave Solutions

The study of nonlinear physical and abstract systems is greatly important in order to determine the behavior of the solutions for Fractional Partial Differential Equations (FPDEs). In this paper, we study the analytical wave solutions of the time-fractional coupled Whitham–Broer–Kaup (WBK) equations under the meaning of conformal fractional derivative. These solutions are derived using the modified extended tanh-function method. Accordingly, different new forms of the solutions are obtained. In order to understand its behavior under varying parameters, we give the visual representations of all the solutions. Finally, the graphs are discussed and a conclusion is given.

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