On convergence of homotopy analysis method and its modification for fractional modified KdV equations

O. Abdulaziz; A. Sami Bataineh; I. Hashim

doi:10.1007/s12190-009-0274-1

On convergence of homotopy analysis method and its modification for fractional modified KdV equations

O. Abdulaziz
, A. Sami Bataineh
, I. Hashim

Universiti Kebangsaan Malaysia

Research output: Contribution to journal › Article › peer-review

12 Scopus citations

Abstract

In this paper, the homotopy analysis method (HAM) and its modification (MHAM) are applied to solve the nonlinear time- and space-fractional modified Korteweg-de Vries (fmKdV). The fractional derivatives are described by Caputo's sense. Approximate and exact analytical solutions of the fmKdV are obtained. The MHAM in particular overcomes the computing difficulty encountered in HAM. Convergence theorems for both the homogeneous and non-homogeneous cases are given. The results of applying this procedure to the studied cases show the high accuracy and efficiency of the approach.

Original language	English
Pages (from-to)	61-81
Number of pages	21
Journal	Journal of Applied Mathematics and Computing
Volume	33
Issue number	1-2
DOIs	https://doi.org/10.1007/s12190-009-0274-1
State	Published - Jun 2010
Externally published	Yes

Keywords

Caputo's fractional derivative
Fractional modified Korteweg-de Vries
Homotopy analysis method

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10.1007/s12190-009-0274-1

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title = "On convergence of homotopy analysis method and its modification for fractional modified KdV equations",

abstract = "In this paper, the homotopy analysis method (HAM) and its modification (MHAM) are applied to solve the nonlinear time- and space-fractional modified Korteweg-de Vries (fmKdV). The fractional derivatives are described by Caputo's sense. Approximate and exact analytical solutions of the fmKdV are obtained. The MHAM in particular overcomes the computing difficulty encountered in HAM. Convergence theorems for both the homogeneous and non-homogeneous cases are given. The results of applying this procedure to the studied cases show the high accuracy and efficiency of the approach.",

keywords = "Caputo's fractional derivative, Fractional modified Korteweg-de Vries, Homotopy analysis method",

author = "O. Abdulaziz and Bataineh, \{A. Sami\} and I. Hashim",

year = "2010",

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doi = "10.1007/s12190-009-0274-1",

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TY - JOUR

T1 - On convergence of homotopy analysis method and its modification for fractional modified KdV equations

AU - Abdulaziz, O.

AU - Bataineh, A. Sami

AU - Hashim, I.

PY - 2010/6

Y1 - 2010/6

N2 - In this paper, the homotopy analysis method (HAM) and its modification (MHAM) are applied to solve the nonlinear time- and space-fractional modified Korteweg-de Vries (fmKdV). The fractional derivatives are described by Caputo's sense. Approximate and exact analytical solutions of the fmKdV are obtained. The MHAM in particular overcomes the computing difficulty encountered in HAM. Convergence theorems for both the homogeneous and non-homogeneous cases are given. The results of applying this procedure to the studied cases show the high accuracy and efficiency of the approach.

AB - In this paper, the homotopy analysis method (HAM) and its modification (MHAM) are applied to solve the nonlinear time- and space-fractional modified Korteweg-de Vries (fmKdV). The fractional derivatives are described by Caputo's sense. Approximate and exact analytical solutions of the fmKdV are obtained. The MHAM in particular overcomes the computing difficulty encountered in HAM. Convergence theorems for both the homogeneous and non-homogeneous cases are given. The results of applying this procedure to the studied cases show the high accuracy and efficiency of the approach.

KW - Caputo's fractional derivative

KW - Fractional modified Korteweg-de Vries

KW - Homotopy analysis method

UR - https://www.scopus.com/pages/publications/77952880577

U2 - 10.1007/s12190-009-0274-1

DO - 10.1007/s12190-009-0274-1

M3 - Article

AN - SCOPUS:77952880577

SN - 1598-5865

VL - 33

SP - 61

EP - 81

JO - Journal of Applied Mathematics and Computing

JF - Journal of Applied Mathematics and Computing

IS - 1-2

ER -

On convergence of homotopy analysis method and its modification for fractional modified KdV equations

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Keywords

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