$Homotopy decomposition method for solving higher-order time-fractional diffusion equation via modified beta derivative$

Homotopy decomposition method for solving higher-order time-fractional diffusion equation via modified beta derivative

In this paper, the homotopy decomposition method with a modified definition of beta fractional derivative is adopted to find approximate solutions of higher-dimensional time-fractional diffusion equations. To apply this method, we find the modified beta integral for both sides of a fractional differ...

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Main Authors:	Abuasad, Salah, Ishak Hashim
Format:	Article
Language:	English
Published:	Penerbit Universiti Kebangsaan Malaysia 2018
Online Access:	http://journalarticle.ukm.my/12672/ http://journalarticle.ukm.my/12672/ http://journalarticle.ukm.my/12672/1/33%20Salah%20Abuasad.pdf

id	ukm-12672
recordtype	eprints
spelling	ukm-126722019-03-17T11:55:33Z http://journalarticle.ukm.my/12672/ Homotopy decomposition method for solving higher-order time-fractional diffusion equation via modified beta derivative Abuasad, Salah Ishak Hashim, In this paper, the homotopy decomposition method with a modified definition of beta fractional derivative is adopted to find approximate solutions of higher-dimensional time-fractional diffusion equations. To apply this method, we find the modified beta integral for both sides of a fractional differential equation first, then using homotopy decomposition method we can obtain the solution of the integral equation in a series form. We compare the solutions obtained by the proposed method with the exact solutions obtained using fractional variational homotopy perturbation iteration method via modified Riemann-Liouville derivative. The comparison shows that the results are in a good agreement. Penerbit Universiti Kebangsaan Malaysia 2018-11 Article PeerReviewed application/pdf en http://journalarticle.ukm.my/12672/1/33%20Salah%20Abuasad.pdf Abuasad, Salah and Ishak Hashim, (2018) Homotopy decomposition method for solving higher-order time-fractional diffusion equation via modified beta derivative. Sains Malaysiana, 47 (11). pp. 2899-2905. ISSN 0126-6039 http://www.ukm.my/jsm/malay_journals/jilid47bil11_2018/KandunganJilid47Bil11_2018.html
repository_type	Digital Repository
institution_category	Local University
institution	Universiti Kebangasaan Malaysia
building	UKM Institutional Repository
collection	Online Access
language	English
description	In this paper, the homotopy decomposition method with a modified definition of beta fractional derivative is adopted to find approximate solutions of higher-dimensional time-fractional diffusion equations. To apply this method, we find the modified beta integral for both sides of a fractional differential equation first, then using homotopy decomposition method we can obtain the solution of the integral equation in a series form. We compare the solutions obtained by the proposed method with the exact solutions obtained using fractional variational homotopy perturbation iteration method via modified Riemann-Liouville derivative. The comparison shows that the results are in a good agreement.
format	Article
author	Abuasad, Salah Ishak Hashim,
spellingShingle	Abuasad, Salah Ishak Hashim, Homotopy decomposition method for solving higher-order time-fractional diffusion equation via modified beta derivative
author_facet	Abuasad, Salah Ishak Hashim,
author_sort	Abuasad, Salah
title	Homotopy decomposition method for solving higher-order time-fractional diffusion equation via modified beta derivative
title_short	Homotopy decomposition method for solving higher-order time-fractional diffusion equation via modified beta derivative
title_full	Homotopy decomposition method for solving higher-order time-fractional diffusion equation via modified beta derivative
title_fullStr	Homotopy decomposition method for solving higher-order time-fractional diffusion equation via modified beta derivative
title_full_unstemmed	Homotopy decomposition method for solving higher-order time-fractional diffusion equation via modified beta derivative
title_sort	homotopy decomposition method for solving higher-order time-fractional diffusion equation via modified beta derivative
publisher	Penerbit Universiti Kebangsaan Malaysia
publishDate	2018
url	http://journalarticle.ukm.my/12672/ http://journalarticle.ukm.my/12672/ http://journalarticle.ukm.my/12672/1/33%20Salah%20Abuasad.pdf
first_indexed	2023-09-18T20:03:08Z
last_indexed	2023-09-18T20:03:08Z
_version_	1777406981867307008

Homotopy decomposition method for solving higher-order time-fractional diffusion equation via modified beta derivative

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