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.

Exact solutions for the fractional differential equations by using the first integral method

2015 ◽  
Vol 4 (1) ◽  
Author(s):  
Hossein Aminikhah ◽  
A. Refahi Sheikhani ◽  
Hadi Rezazadeh
Keyword(s):  
Differential Equations ◽  
Exact Solutions ◽  
Fractional Differential Equations ◽  
Commutative Algebra ◽  
Integral Method ◽  
First Integral ◽  
Ring Theory ◽  
First Integral Method ◽  
Fractional Differential ◽  
Method Show

AbstractIn this paper, we apply the first integral method to study the solutions of the nonlinear fractional modified Benjamin-Bona-Mahony equation, the nonlinear fractional modified Zakharov-Kuznetsov equation and the nonlinear fractional Whitham-Broer-Kaup-Like systems. This method is based on the ring theory of commutative algebra. The results obtained by the proposed method show that the approach is effective and general. This approach can also be applied to other nonlinear fractional differential equations, which are arising in the theory of solitons and other areas.

scholarly journals New exact solutions of the space-time fractional KdV-burgers and nonlinear fractional foam drainage equation

2018 ◽  
Vol 22 (Suppl. 1) ◽  
pp. 15-24 ◽  
Author(s):  
Adem Cevikel
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
First Integral ◽  
Solution Procedure ◽  
First Integral Method ◽  
Fractional Complex Transform ◽  
New Exact Solutions ◽  
Fractional Differential ◽  
Linear Differential ◽  
Foam Drainage Equation

The fractional differential equations have been studied by many authors and some effective methods for fractional calculus were appeared in literature, such as the fractional sub-equation method and the first integral method. The fractional complex transform approach is to convert the fractional differential equations into ordinary differential equations, making the solution procedure simple. Recently, the fractional complex transform has been suggested to convert fractional order differential equations with modified Riemann-Liouville derivatives into integer order differential equations, and the reduced equations can be solved by symbolic computation. The present paper investigates for the applicability and efficiency of the exp-function method on some fractional non-linear differential equations.

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.

First integral method for non-linear differential equations with conformable derivative

2018 ◽  
Vol 13 (1) ◽  
pp. 14 ◽  
Author(s):  
H. Yépez-Martínez ◽  
J.F. Gómez-Aguilar ◽  
Abdon Atangana
Keyword(s):  
Differential Equations ◽  
Exact Solutions ◽  
Integral Method ◽  
General Scheme ◽  
First Integral ◽  
Fractional Partial Differential Equations ◽  
Conformable Derivative ◽  
First Integral Method ◽  
Analytic Treatment ◽  
Linear Differential

In this paper, we present an analysis based on the first integral method in order to construct exact solutions of the nonlinear fractional partial differential equations (FPDE) described by beta-derivative. A general scheme to find the approximated solutions of the nonlinear FPDE is showed. The results obtained showed that the first integral method is an efficient technique for analytic treatment of nonlinear beta-derivative FPDE.

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