Approximate analytical solution for the fractional modified KdV by differential transform method

被引：67

作者：

Kurulay, Muhammet ^{[1
]}

Bayram, Mustafa ^{[2
]}

机构：

[1] Yildiz Tekn Univ, Fac Art & Sci, Dept Math, TR-34210 Davutpasa, Turkey

[2] Fatih Univ, Fac Arts & Sci, Dept Math, TR-34500 Istanbul, Turkey

来源：

COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION | 2010年 / 15卷 / 07期

关键词：

Fractional differential equation; Caputo fractional derivative; Differential transform method; fmKdV; fKdV; ADOMIAN DECOMPOSITION METHOD; HOMOTOPY ANALYSIS METHOD; GENERALIZED TAYLORS FORMULA; DIFFUSION-WAVE EQUATION; NUMERICAL-SOLUTIONS; BURGERS EQUATION; ORDER; SYSTEM;

D O I：

10.1016/j.cnsns.2009.07.014

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, the fractional modified Korteweg-de Vries equation (fmKdV) and fKdV are introduced by fractional derivatives. The approach rest mainly on two-dimensional differential transform method (DTM) which is one of the approximate methods. The method can easily be applied to many problems and is capable of reducing the size of computational work. The fractional derivative is described in the Caputo sense. Some illustrative examples are presented. Crown Copyright (c) 2009 Published by Elsevier B.V. All rights reserved.

引用

页码：1777 / 1782

页数：6

共 28 条

[1] Approximate analytical solution to fractional modified KdV equations [J].

Abdulaziz, O. ;

Hashim, I. ;

Ismail, E. S. .

MATHEMATICAL AND COMPUTER MODELLING, 2009, 49 (1-2) :136-145

[2]

[Anonymous], 1999, APPL FRACTIONAL CALC

[3]

[Anonymous], 1999, FRACTIONAL DIFFERENT

[4]

[Anonymous], 2016, INT J NONLIN SCI NUM, DOI DOI 10.1515/IJNSNS.2006.7.1.27

[5] Solution of fractional differential equations by using differential transform method [J].

Arikoglu, Aytac ;

Ozkol, Ibrahim .

CHAOS SOLITONS & FRACTALS, 2007, 34 (05) :1473-1481

[6] Series Solutions of Systems of Nonlinear Fractional Differential Equations [J].

Bataineh, A. S. ;

Alomari, A. K. ;

Noorani, M. S. M. ;

Hashim, I. ;

Nazar, R. .

ACTA APPLICANDAE MATHEMATICAE, 2009, 105 (02) :189-198

[7] Solution of different type of the partial differential equation by differential transform method and Adomian's decomposition method [J].

Bildik, N ;

Konuralp, A ;

Bek, FO ;

Küçükarslan, S .

APPLIED MATHEMATICS AND COMPUTATION, 2006, 172 (01) :551-567

[8] 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-&

[9] Comparison differential transformation technique with Adomian decomposition method for linear and nonlinear initial value problems [J].

Hassan, I. H. Abdel-Halim .

CHAOS SOLITONS & FRACTALS, 2008, 36 (01) :53-65

[10] A note on the use of Adomian decomposition method for high-order and system of nonlinear differential equations [J].

Hosseini, M. M. ;

Jafari, M. .

COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, 2009, 14 (05) :1952-1957

← 1 2 3 →