scholarly journals The first integral method and its application for finding the exact solutions of nonlinear fractional partial differential equations (PDES) in the mathematical physics

2014 ◽  
Vol 9 (8) ◽  
pp. 174-183 ◽  
Author(s):  
M. E. Zayed Elsayed ◽  
A. Amer Yasser
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Exact Solutions ◽  
Integral Method ◽  
First Integral ◽  
Mathematical Physics ◽  
Fractional Partial Differential Equations ◽  
Partial Differential ◽  
First Integral Method

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.

scholarly journals New Exact Solutions of Some Nonlinear Systems of Partial Differential Equations Using the First Integral Method

2013 ◽  
Vol 2013 ◽  
pp. 1-13 ◽  
Author(s):  
Shoukry Ibrahim Atia El-Ganaini
Keyword(s):  
Partial Differential Equations ◽  
Nonlinear Systems ◽  
Differential Equations ◽  
Integral Method ◽  
Traveling Wave Solutions ◽  
First Integral ◽  
First Integrals ◽  
Partial Differential ◽  
First Integral Method ◽  
New Exact Solutions

The first integral method introduced by Feng is adopted for solving some important nonlinear systems of partial differential equations, including classical Drinfel'd-Sokolov-Wilson system (DSWE), (2 + 1)-dimensional Davey-Stewartson system, and generalized Hirota-Satsuma coupled KdV system. This method provides polynomial first integrals for autonomous planar systems. Through the established first integrals, exact traveling wave solutions are formally derived in a concise manner. This method can also be applied to nonintegrable equations as well as integrable ones.

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