Note on the Convergence Analysis of Homotopy Perturbation Method for Fractional Partial Differential Equations

We apply the homotopy perturbation method to obtain the solution of partial differential equations of fractional order. This method is powerful tool to find exact and approximate solution of many linear and nonlinear partial differential equations of fractional order. Convergence of the method is pr...

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Main Authors: Asma Ali Elbeleze, Adem Kılıçman, Bachok M. Taib
Format: Article
Language:English
Published: Wiley 2014-01-01
Series:Abstract and Applied Analysis
Online Access:http://dx.doi.org/10.1155/2014/803902
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author Asma Ali Elbeleze
Adem Kılıçman
Bachok M. Taib
author_facet Asma Ali Elbeleze
Adem Kılıçman
Bachok M. Taib
author_sort Asma Ali Elbeleze
collection DOAJ
description We apply the homotopy perturbation method to obtain the solution of partial differential equations of fractional order. This method is powerful tool to find exact and approximate solution of many linear and nonlinear partial differential equations of fractional order. Convergence of the method is proved and the convergence analysis is reliable enough to estimate the maximum absolute truncated error of the series solution. The fractional derivatives are described in the Caputo sense. Some examples are presented to verify convergence hypothesis and simplicity of the method.
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spelling doaj-art-e4dfdae2c7b244b18f8606e0510fb2b82025-08-20T02:21:18ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/803902803902Note on the Convergence Analysis of Homotopy Perturbation Method for Fractional Partial Differential EquationsAsma Ali Elbeleze0Adem Kılıçman1Bachok M. Taib2Faculty of Science and Technology, Universiti Sains Islam Malaysia (USIM), 71800 Nilai, MalaysiaDepartment of Mathematics and Institute for Mathematical Research, University Putra Malaysia, 43400 Serdang, Selangor, MalaysiaFaculty of Science and Technology, Universiti Sains Islam Malaysia (USIM), 71800 Nilai, MalaysiaWe apply the homotopy perturbation method to obtain the solution of partial differential equations of fractional order. This method is powerful tool to find exact and approximate solution of many linear and nonlinear partial differential equations of fractional order. Convergence of the method is proved and the convergence analysis is reliable enough to estimate the maximum absolute truncated error of the series solution. The fractional derivatives are described in the Caputo sense. Some examples are presented to verify convergence hypothesis and simplicity of the method.http://dx.doi.org/10.1155/2014/803902
spellingShingle Asma Ali Elbeleze
Adem Kılıçman
Bachok M. Taib
Note on the Convergence Analysis of Homotopy Perturbation Method for Fractional Partial Differential Equations
Abstract and Applied Analysis
title Note on the Convergence Analysis of Homotopy Perturbation Method for Fractional Partial Differential Equations
title_full Note on the Convergence Analysis of Homotopy Perturbation Method for Fractional Partial Differential Equations
title_fullStr Note on the Convergence Analysis of Homotopy Perturbation Method for Fractional Partial Differential Equations
title_full_unstemmed Note on the Convergence Analysis of Homotopy Perturbation Method for Fractional Partial Differential Equations
title_short Note on the Convergence Analysis of Homotopy Perturbation Method for Fractional Partial Differential Equations
title_sort note on the convergence analysis of homotopy perturbation method for fractional partial differential equations
url http://dx.doi.org/10.1155/2014/803902
work_keys_str_mv AT asmaalielbeleze noteontheconvergenceanalysisofhomotopyperturbationmethodforfractionalpartialdifferentialequations
AT ademkılıcman noteontheconvergenceanalysisofhomotopyperturbationmethodforfractionalpartialdifferentialequations
AT bachokmtaib noteontheconvergenceanalysisofhomotopyperturbationmethodforfractionalpartialdifferentialequations