Analytical Approach for the Space-time Nonlinear Partial Differential Fractional Equation

2014 ◽  
Vol 15 (7-8) ◽  
Author(s):  
Ahmet Bekir ◽  
Özkan Güner
Keyword(s):  
Function Method ◽  
Analytical Approach ◽  
Fractional Derivatives ◽  
Space Time ◽  
Variable Method ◽  
Partial Differential ◽  
Functional Variable ◽  
Liouville Derivative ◽  
Functional Variable Method ◽  
Fractional Equation

AbstractIn this paper, the fractional derivatives in the sense of modified Riemann–Liouville derivative and the functional variable method, exp-function method and

scholarly journals Travelling wave solutions of nonlinear systems of PDEs by using the functional variable method

2015 ◽  
Vol 34 (2) ◽  
pp. 213-229 ◽  
Author(s):  
Hossein Aminikhah ◽  
Amir Hosein Refahi Sheikhani ◽  
Hadi Rezazadeh
Keyword(s):  
Partial Differential Equations ◽  
Nonlinear Systems ◽  
Differential Equations ◽  
Travelling Wave ◽  
Variable Method ◽  
Boussinesq System ◽  
Wave Transformation ◽  
Partial Differential ◽  
Functional Variable ◽  
Functional Variable Method

In this paper, we will use the functional variable method to construct exact solutions of some nonlinear systems of partial differential equations, including, the (2+1)-dimensional Bogoyavlenskii’s breaking soliton equation, the WhithamBroer-Kaup-Like systems and the Kaup-Boussinesq system. This approach can also be applied to other nonlinear systems of partial differential equations which can be converted to a second-order ordinary differential equation through the travelling wave transformation.

scholarly journals Exp-Function Method for Solving Fractional Partial Differential Equations

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Bin Zheng
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Exact Solutions ◽  
Function Method ◽  
Space Time ◽  
Fractional Partial Differential Equations ◽  
Partial Differential ◽  
New Exact Solutions ◽  
Complex Transformation ◽  
Liouville Derivative

We extend the Exp-function method to fractional partial differential equations in the sense of modified Riemann-Liouville derivative based on nonlinear fractional complex transformation. For illustrating the validity of this method, we apply it to the space-time fractional Fokas equation and the nonlinear fractional Sharma-Tasso-Olver (STO) equation. As a result, some new exact solutions for them are successfully established.

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