scholarly journals The Extended Fractional Subequation Method for Nonlinear Fractional Differential Equations

2012 ◽  
Vol 2012 ◽  
pp. 1-11 ◽  
Author(s):  
Jianping Zhao ◽  
Bo Tang ◽  
Sunil Kumar ◽  
Yanren Hou
Keyword(s):  
Differential Equations ◽  
Exact Solutions ◽  
Riccati Equation ◽  
Fractional Differential Equations ◽  
Space Time ◽  
Mathematical Tool ◽  
Nonlinear Fractional Differential Equations ◽  
Burgers Equations ◽  
Fractional Differential ◽  
Powerful Mathematical Tool

An extended fractional subequation method is proposed for solving fractional differential equations by introducing a new general ansätz and Bäcklund transformation of the fractional Riccati equation with known solutions. Being concise and straightforward, this method is applied to the space-time fractional coupled Burgers’ equations and coupled MKdV equations. As a result, many exact solutions are obtained. It is shown that the considered method provides a very effective, convenient, and powerful mathematical tool for solving fractional differential equations.

The First Integral Method for Exact Solutions of Nonlinear Fractional Differential Equations

2015 ◽  
Vol 10 (2) ◽  
Author(s):  
Ahmet Bekir ◽  
Özkan Güner ◽  
Ömer Ünsal
Keyword(s):  
Differential Equations ◽  
Exact Solutions ◽  
Fractional Differential Equations ◽  
Integral Method ◽  
First Integral ◽  
Space Time ◽  
First Integral Method ◽  
Nonlinear Fractional Differential Equations ◽  
Fractional Complex Transform ◽  
Fractional Differential

In this paper, we establish exact solutions for some nonlinear fractional differential equations (FDEs). The first integral method with help of the fractional complex transform (FCT) is used to obtain exact solutions for the time fractional modified Korteweg–de Vries (fmKdV) equation and the space–time fractional modified Benjamin–Bona–Mahony (fmBBM) equation. This method is efficient and powerful in solving kind of other nonlinear FDEs.

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 Exact solutions of the space-time fractional equal width equation

2019 ◽  
Vol 23 (4) ◽  
pp. 2307-2313 ◽  
Author(s):  
Hongcai Ma ◽  
Xiangmin Meng ◽  
Hanfang Wu ◽  
Aiping Deng
Keyword(s):  
Differential Equations ◽  
Exact Solutions ◽  
Fractional Differential Equations ◽  
Soliton Solutions ◽  
Space Time ◽  
Bright Soliton ◽  
Liouville Derivative ◽  
Fractional Differential

A class of fractional differential equations is investigated in this paper. By the use of modified Remann-Liouville derivative and the tanh-sech method, the exact bright soliton solutions for the space-time fractional equal width are obtained.

scholarly journals Implicit nonlinear fractional differential equations of variable order

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Amar Benkerrouche ◽  
Mohammed Said Souid ◽  
Kanokwan Sitthithakerngkiet ◽  
Ali Hakem
Keyword(s):  
Differential Equations ◽  
Boundary Value Problem ◽  
Fractional Differential Equations ◽  
Boundary Value ◽  
Variable Order ◽  
Stability Of Solutions ◽  
Nonlinear Fractional Differential Equations ◽  
Caputo Fractional Differential Equations ◽  
Fractional Differential ◽  
The Stability

AbstractIn this manuscript, we examine both the existence and the stability of solutions to the implicit boundary value problem of Caputo fractional differential equations of variable order. We construct an example to illustrate the validity of the observed results.

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