New Exact Solutions of Fractional Differential Equations by (G′/G)-Expansion Method and Improved (G′/G)-Expansion Method

2018 ◽  
pp. 145-181
Author(s):  
Santanu Saha Ray ◽  
Subhadarshan Sahoo
Keyword(s):  
Differential Equations ◽  
Exact Solutions ◽  
Fractional Differential Equations ◽  
Expansion Method ◽  
New Exact Solutions ◽  
Fractional Differential

scholarly journals Exact Solutions of the Space-Time Fractional Bidirectional Wave Equations Using the(G′/G)-Expansion Method

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Wei Li ◽  
Huizhang Yang ◽  
Bin He
Keyword(s):  
Differential Equations ◽  
Exact Solutions ◽  
Fractional Differential Equations ◽  
Wave Equations ◽  
Rational Functions ◽  
Expansion Method ◽  
Space Time ◽  
Promising Tool ◽  
Liouville Derivative ◽  
Fractional Differential

Based on Jumarie’s modified Riemann-Liouville derivative, the fractional complex transformation is used to transform fractional differential equations to ordinary differential equations. Exact solutions including the hyperbolic functions, the trigonometric functions, and the rational functions for the space-time fractional bidirectional wave equations are obtained using the(G′/G)-expansion method. The method provides a promising tool for solving nonlinear fractional differential equations.

scholarly journals Fractional Complex Transform and exp-Function Methods for Fractional Differential Equations

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Ahmet Bekir ◽  
Özkan Güner ◽  
Adem C. Cevikel
Keyword(s):  
Differential Equations ◽  
Exact Solutions ◽  
Ordinary Differential Equations ◽  
Fractional Differential Equations ◽  
Function Method ◽  
Fractional Derivatives ◽  
Fractional Complex Transform ◽  
Fractional Equations ◽  
New Exact Solutions ◽  
Fractional Differential

The exp-function method is presented for finding the exact solutions of nonlinear fractional equations. New solutions are constructed in fractional complex transform to convert fractional differential equations into ordinary differential equations. The fractional derivatives are described in Jumarie's modified Riemann-Liouville sense. We apply the exp-function method to both the nonlinear time and space fractional differential equations. As a result, some new exact solutions for them are successfully established.

scholarly journals A Procedure to Construct Exact Solutions of Nonlinear Fractional Differential Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Özkan Güner ◽  
Adem C. Cevikel
Keyword(s):  
Differential Equations ◽  
Exact Solutions ◽  
Fractional Differential Equations ◽  
Function Method ◽  
Burgers Equation ◽  
Fractional Partial Differential Equations ◽  
New Exact Solutions ◽  
Liouville Derivative ◽  
Fractional Differential ◽  
Partial Fractional Differential Equations

We use the fractional transformation to convert the nonlinear partial fractional differential equations with the nonlinear ordinary differential equations. The Exp-function method is extended to solve fractional partial differential equations in the sense of the modified Riemann-Liouville derivative. We apply the Exp-function method to the time fractional Sharma-Tasso-Olver equation, the space fractional Burgers equation, and the time fractional fmKdV equation. As a result, we obtain some new exact solutions.

scholarly journals Exact solutions of conformable fractional differential equations

2021 ◽  
Vol 22 ◽  
pp. 103916
Author(s):  
Haleh Tajadodi ◽  
Zareen A. Khan ◽  
Ateeq ur Rehman Irshad ◽  
J.F. Gómez-Aguilar ◽  
Aziz Khan ◽  
...  
Keyword(s):  
Differential Equations ◽  
Exact Solutions ◽  
Fractional Differential Equations ◽  
Fractional Differential
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