Browsing Mathematics / Matematik by Subject "(G′/G)expansion method"
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An analytic approach to a class of fractional differentialdifference equations of rational type via symbolic computation
(Wiley, 201501)Fractional derivatives are powerful tools in solving the problems of science and engineering. In this paper, an analytical algorithm for solving fractional differentialdifference equations in the sense of Jumarie's modified ... 
Analytic investigation of a reactionDiffusion brusselator model with the timespace fractional derivative
(De Gruyter, 201404)It is well known that many models in nonlinear science are described by fractional differential equations in which an unknown function appears under the operation of a derivative of fractional order. In this study, we ... 
Analytic study on two nonlinear evolution equations by using the (G′/G)expansion method
(Elsevier, 200903)The validity and reliability of the socalled (G′/G)expansion method is tested by applying it to two nonlinear evolutionary equations. Solutions in more general forms are obtained. When the parameters are taken as special ... 
Comment on: The (G'/G)expansion method for the nonlinear lattice equations [Commun Nonlinear Sci Numer Simulat 17 (2012) 34903498]
(Elsevier, 201212)We show that two of the nonlinear lattice equations studied by Ayhan & Bekir [Commun Nonlinear Sci Numer Simulat 17 (2012) 34903498] have already been investigated by Aslan [Commun Nonlinear Sci Numer Simulat 15 (2010) ... 
The discrete (G′/G)expansion method applied to the differentialdifference Burgers equation and the relativistic Toda lattice system
(Wiley, 201201)We introduce the discrete (G′/G)expansion method for solving nonlinear differentialdifference equations (NDDEs). As illustrative examples, we consider the differentialdifference Burgers equation and the relativistic ... 
Discrete exact solutions to some nonlinear differentialdifference equations via the (G′/G)expansion method
(Elsevier, 200912)We extended the (G′/G)expansion method to two wellknown nonlinear differentialdifference equations, the discrete nonlinear Schrödinger equation and the Toda lattice equation, for constructing traveling wave solutions. ... 
Exact and explicit solutions to some nonlinear evolution equations by utilizing the (G′/G)expansion method
(Elsevier, 200909)In this paper, we demonstrate the effectiveness of the socalled (G′/G)expansion method by examining some nonlinear evolution equations with physical interest. Our work is motivated by the fact that the (G′/G)expansion ... 
Exact and explicit solutions to the discrete nonlinear Schrödinger equation with a saturable nonlinearity
(Elsevier, 20111114)We analyze the discrete nonlinear Schrödinger equation with a saturable nonlinearity through the (G′/G)expansion method to present some improved results. Three types of analytic solutions with arbitrary parameters are ... 
Exact solutions for fractional DDEs via auxiliary equation method coupled with the fractional complex transform
(Wiley, 201612)Dynamical behavior of many nonlinear systems can be described by fractionalorder equations. This study is devoted to fractional differential–difference equations of rational type. Our focus is on the construction of exact ... 
The extended discrete (G′/G)expansion method and its application to the relativistic toda lattice system
(American Institute of Physics Publising, 2009)We propose the extended discrete (G′/G)expansion method for directly solving nonlinear differentialdifference equations. For illustration, we choose the relativistic Toda lattice system. We derive further discrete hyperbolic ... 
A note on the (G′/G)expansion method again
(Elsevier, 201009)We report an observation on two recent analytic methods; the (G′/G)expansion method and the simplest equation method. © 2010 Elsevier Inc. All rights reserved. 
On the validity and reliability of the (G′/G)expansion method by using higherorder nonlinear equations
(Elsevier, 200905)In this study, we demonstrate the validity and reliability of the socalled (G′/G)expansion method via symbolic computation. For illustrative examples, we choose the sixthorder Boussinesq equation and the ninthorder ... 
Some exact solutions for Toda type lattice differential equations using the improved (G′/G)expansion method
(Wiley, 201203)Nonlinear lattice differential equations (also known as differentialdifference equations) appear in many applications. They can be thought of as hybrid systems for the inclusion of both discrete and continuous variables. ... 
Symbolic computation and construction of new exact traveling wave solutions to FitzhughNagumo and KleinGordon equations
(Verlag der Zeitschrift für Naturforschung, 2009)With the aid of the symbolic computation system Mathematica, many exact solutions for the FitzhughNagumo equation and the KleinGordon equation with a quadratic nonlinearity are constructed by an auxiliary equation method, ... 
Symbolic computation of exact solutions for fractional differentialdifference equation models
(Vilnius University Institute of Mathematics and Informatics, 201411)The aim of the present study is to extend the (G′=G)expansion method to fractional differentialdifference equations of rational type. Particular timefractional models are considered to show the strength of the method. ...