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

O. Abdulaziz, A. Sami Bataineh, Ishak Hashim

Research output: Contribution to journalArticle

9 Citations (Scopus)

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 languageEnglish
Pages (from-to)61-81
Number of pages21
JournalJournal of Applied Mathematics and Computing
Volume33
Issue number1-2
DOIs
Publication statusPublished - Jun 2010

Fingerprint

Homotopy Analysis Method
KdV Equation
Modified Equations
Fractional
Derivatives
Fractional Derivative
Convergence Theorem
High Efficiency
Analytical Solution
High Accuracy
Computing

Keywords

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

ASJC Scopus subject areas

  • Applied Mathematics
  • Computational Mathematics

Cite this

On convergence of homotopy analysis method and its modification for fractional modified KdV equations. / Abdulaziz, O.; Bataineh, A. Sami; Hashim, Ishak.

In: Journal of Applied Mathematics and Computing, Vol. 33, No. 1-2, 06.2010, p. 61-81.

Research output: Contribution to journalArticle

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