Fractional Complex Transform and exp-Function Methods for Fractional Differential Equations

被引：131

作者：

Bekir, Ahmet ^{[1
]}

Guner, Ozkan ^{[2
]}

Cevikel, Adem C. ^{[3
]}

机构：

[1] Eskisehir Osmangazi Univ, Art Sci Fac, Dept Math & Comp Sci, TR-26480 Eskisehir, Turkey

[2] Dumlupinar Univ, Sch Appl Sci, Dept Management Informat Syst, TR-43100 Kutahya, Turkey

[3] Yildiz Tech Univ, Fac Educ, Dept Math Educ, TR-34220 Istanbul, Turkey

来源：

ABSTRACT AND APPLIED ANALYSIS | 2013年

关键词：

NONLINEAR EVOLUTION-EQUATIONS; CAHN-HILLIARD EQUATION; VARIABLE-COEFFICIENTS; MATHEMATICAL PHYSICS; PERIODIC-SOLUTIONS; CALCULUS; MODELS;

D O I：

10.1155/2013/426462

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The exp-function method is presented for finding the exact solutions of nonlinear fractional equations. New solutions are constructed in fractional complex transform to convert fractional differential equations into ordinary differential equations. The fractional derivatives are described in Jumarie's modified Riemann-Liouville sense. We apply the exp-function method to both the nonlinear time and space fractional differential equations. As a result, some new exact solutions for them are successfully established.

引用

页数：8

共 35 条

[1]

[Anonymous], 2006, THEORY APPL FRACTION

[2]

[Anonymous], 1993, INTRO FRACTIONAL CA

[3] New solitons and periodic solutions for nonlinear physical models in mathematical physics [J].

Bekir, Ahmet ;

Cevikel, Adem C. .

NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, 2010, 11 (04) :3275-3285

[4] Application of the Exp-function method for nonlinear differential-difference equations [J].

Bekir, Ahmet .

APPLIED MATHEMATICS AND COMPUTATION, 2010, 215 (11) :4049-4053

[5]

Bekir A, 2009, INT J NONLIN SCI NUM, V10, P735

[6] LINEAR MODELS OF DISSIPATION WHOSE Q IS ALMOST FREQUENCY INDEPENDENT-2 [J].

CAPUTO, M .

GEOPHYSICAL JOURNAL OF THE ROYAL ASTRONOMICAL SOCIETY, 1967, 13 (05) :529-&

[7] A conservative difference scheme for the viscous Cahn-Hilliard equation with a nonconstant gradient energy coefficient [J].

Choo, SM ;

Chung, SK ;

Lee, YJ .

APPLIED NUMERICAL MATHEMATICS, 2004, 51 (2-3) :207-219

[8] New analytic solutions of stochastic coupled KdV equations [J].

Dai, Chaoqing ;

Chen, Junlang .

CHAOS SOLITONS & FRACTALS, 2009, 42 (04) :2200-2207

[9] Exact solitary wave solutions for some nonlinear evolution equations via Exp-function method [J].

Ebaid, A. .

PHYSICS LETTERS A, 2007, 365 (03) :213-219

[10] Exact Solutions of Fractional-Order Biological Population Model [J].

El-Sayed, A. M. A. ;

Rida, S. Z. ;

Arafa, A. A. M. .

COMMUNICATIONS IN THEORETICAL PHYSICS, 2009, 52 (06) :992-996

← 1 2 3 4 →