Numerical solution of fractional Mathieu equations by using block-pulse wavelets

Numerical solution of fractional Mathieu equations by using block-pulse wavelets

In this paper, we introduce a method based on operational matrix of fractional order integration for the numerical solution of fractional Mathieu equation and then apply it in a number of cases. For this, we use the block-pulse wavelets matrix of fractional order integration with respect to the Capu...

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Main Authors: P. Pirmohabbati, A.H. Refahi Sheikhani, H. Saberi Najafi, A. Abdolahzadeh Ziabari
Format: Article
Language:English
Published: Elsevier 2019-12-01
Series:Journal of Ocean Engineering and Science
Online Access:http://www.sciencedirect.com/science/article/pii/S2468013319300439
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spelling doaj-d3a39c796472478d81c8ed9e226717ce2020-11-25T01:38:57ZengElsevierJournal of Ocean Engineering and Science2468-01332019-12-0144299307Numerical solution of fractional Mathieu equations by using block-pulse waveletsP. Pirmohabbati0A.H. Refahi Sheikhani1H. Saberi Najafi2A. Abdolahzadeh Ziabari3Department of Applied Mathematics, Faculty of Mathematical Sciences, Lahijan Branch, Islamic Azad University, Lahijan, IranCorresponding author.; Department of Applied Mathematics, Faculty of Mathematical Sciences, Lahijan Branch, Islamic Azad University, Lahijan, IranDepartment of Applied Mathematics, Faculty of Mathematical Sciences, Lahijan Branch, Islamic Azad University, Lahijan, IranDepartment of physics, Faculty of Science, Lahidjan Branch, Islamic Azad University, Lahidjan, IranIn this paper, we introduce a method based on operational matrix of fractional order integration for the numerical solution of fractional Mathieu equation and then apply it in a number of cases. For this, we use the block-pulse wavelets matrix of fractional order integration with respect to the Caputo sense. The method was tested by some numerical examples and changes occurred in the coefficients as well as in the derivative of the equation. Results prove the accuracy and computational efficiency of the proposed algorithm. Keywords: Block-pulse functions, Fractional calculus, Mathieu differential equation, MSC: 26A33, 93D20, 97N40, 34A08http://www.sciencedirect.com/science/article/pii/S2468013319300439
collection DOAJ
language English
format Article
sources DOAJ
author P. Pirmohabbati
A.H. Refahi Sheikhani
H. Saberi Najafi
A. Abdolahzadeh Ziabari
spellingShingle P. Pirmohabbati
A.H. Refahi Sheikhani
H. Saberi Najafi
A. Abdolahzadeh Ziabari
Numerical solution of fractional Mathieu equations by using block-pulse wavelets
Journal of Ocean Engineering and Science
author_facet P. Pirmohabbati
A.H. Refahi Sheikhani
H. Saberi Najafi
A. Abdolahzadeh Ziabari
author_sort P. Pirmohabbati
title Numerical solution of fractional Mathieu equations by using block-pulse wavelets
title_short Numerical solution of fractional Mathieu equations by using block-pulse wavelets
title_full Numerical solution of fractional Mathieu equations by using block-pulse wavelets
title_fullStr Numerical solution of fractional Mathieu equations by using block-pulse wavelets
title_full_unstemmed Numerical solution of fractional Mathieu equations by using block-pulse wavelets
title_sort numerical solution of fractional mathieu equations by using block-pulse wavelets
publisher Elsevier
series Journal of Ocean Engineering and Science
issn 2468-0133
publishDate 2019-12-01
description In this paper, we introduce a method based on operational matrix of fractional order integration for the numerical solution of fractional Mathieu equation and then apply it in a number of cases. For this, we use the block-pulse wavelets matrix of fractional order integration with respect to the Caputo sense. The method was tested by some numerical examples and changes occurred in the coefficients as well as in the derivative of the equation. Results prove the accuracy and computational efficiency of the proposed algorithm. Keywords: Block-pulse functions, Fractional calculus, Mathieu differential equation, MSC: 26A33, 93D20, 97N40, 34A08
url http://www.sciencedirect.com/science/article/pii/S2468013319300439
work_keys_str_mv AT ppirmohabbati numericalsolutionoffractionalmathieuequationsbyusingblockpulsewavelets
AT ahrefahisheikhani numericalsolutionoffractionalmathieuequationsbyusingblockpulsewavelets
AT hsaberinajafi numericalsolutionoffractionalmathieuequationsbyusingblockpulsewavelets
AT aabdolahzadehziabari numericalsolutionoffractionalmathieuequationsbyusingblockpulsewavelets
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