scholarly journals A Table Lookup Method for Exact Analytical Solutions of Nonlinear Fractional Partial Differential Equations

2017 ◽  
Vol 2017 ◽  
pp. 1-14
Author(s):  
Ji Juan-Juan ◽  
Guo Ye-Cai ◽  
Zhang Lan-Fang ◽  
Zhang Chao-Long
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Analytical Solutions ◽  
Space Time ◽  
Hyperbolic Function ◽  
Fractional Partial Differential Equations ◽  
Partial Differential ◽  
Table Lookup ◽  
Exact Analytical Solutions ◽  
Function Solution

A table lookup method for solving nonlinear fractional partial differential equations (fPDEs) is proposed in this paper. Looking up the corresponding tables, we can quickly obtain the exact analytical solutions of fPDEs by using this method. To illustrate the validity of the method, we apply it to construct the exact analytical solutions of four nonlinear fPDEs, namely, the time fractional simplified MCH equation, the space-time fractional combined KdV-mKdV equation, the (2+1)-dimensional time fractional Zoomeron equation, and the space-time fractional ZKBBM equation. As a result, many new types of exact analytical solutions are obtained including triangular periodic solution, hyperbolic function solution, singular solution, multiple solitary wave solution, and Jacobi elliptic function solution.

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 Improved Fractional Subequation Method and Exact Solutions to Fractional Partial Differential Equations

2020 ◽  
Vol 2020 ◽  
pp. 1-18
Author(s):  
Jun Jiang ◽  
Yuqiang Feng ◽  
Shougui Li
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Exact Solutions ◽  
Burgers Equation ◽  
Space Time ◽  
Fractional Partial Differential Equations ◽  
Partial Differential ◽  
Biological Population ◽  
Regularized Long Wave Equation ◽  
Generalized Time

In this paper, the improved fractional subequation method is applied to establish the exact solutions for some nonlinear fractional partial differential equations. Solutions to the generalized time fractional biological population model, the generalized time fractional compound KdV-Burgers equation, the space-time fractional regularized long-wave equation, and the (3+1)-space-time fractional Zakharov-Kuznetsov equation are obtained, respectively.

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