scholarly journals A new fractional Jacobi elliptic equation method for solving fractional partial differential equations

2014 ◽  
Vol 2014 (1) ◽  
Author(s):  
Bin Zheng
Keyword(s):  
Partial Differential Equations ◽  
Elliptic Equation ◽  
Differential Equations ◽  
Equation Method ◽  
Fractional Partial Differential Equations ◽  
Partial Differential

scholarly journals The Jacobi Elliptic Equation Method for Solving Fractional Partial Differential Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Bin Zheng ◽  
Qinghua Feng
Keyword(s):  
Partial Differential Equations ◽  
Elliptic Equation ◽  
Differential Equations ◽  
Exact Solutions ◽  
Equation Method ◽  
Hyperbolic Function ◽  
Jacobi Elliptic Function ◽  
Fractional Partial Differential Equations ◽  
Partial Differential ◽  
Liouville Derivative

Based on a nonlinear fractional complex transformation, the Jacobi elliptic equation method is extended to seek exact solutions for fractional partial differential equations in the sense of the modified Riemann-Liouville derivative. For demonstrating the validity of this method, we apply it to solve the space fractional coupled Konopelchenko-Dubrovsky (KD) equations and the space-time fractional Fokas equation. As a result, some exact solutions for them including the hyperbolic function solutions, trigonometric function solutions, rational function solutions, and Jacobi elliptic function solutions are successfully found.

scholarly journals Exact solutions of non-linear fractional partial differential equations by fractional sub-equation method

2015 ◽  
Vol 19 (4) ◽  
pp. 1239-1244 ◽  
Author(s):  
Hong-Cai Ma ◽  
Dan-Dan Yao ◽  
Xiao-Fang Peng
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Exact Solutions ◽  
Space Time ◽  
Equation Method ◽  
Fractional Partial Differential Equations ◽  
Partial Differential ◽  
Non Linear

This paper studies the space-time fractional Whitham-Broer-Kaup equations by the existed fractional sub-equation method, and exact solutions are obtained.

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