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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| Format: | Article |
| Language: | en |
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Penerbit Universiti Kebangsaan Malaysia
2018
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| Online Access: | http://journalarticle.ukm.my/12672/1/33%20Salah%20Abuasad.pdf http://journalarticle.ukm.my/12672/ http://www.ukm.my/jsm/malay_journals/jilid47bil11_2018/KandunganJilid47Bil11_2018.html |
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| _version_ | 1834431939602284544 |
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| author | Abuasad, Salah Ishak Hashim, |
| author_facet | Abuasad, Salah Ishak Hashim, |
| author_sort | Abuasad, Salah |
| building | Tun Sri Lanang Library |
| collection | Institutional Repository |
| content_provider | Universiti Kebangsaan Malaysia |
| content_source | UKM Journal Article Repository |
| continent | Asia |
| country | Malaysia |
| 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 |
| id | my-ukm.journal.12672 |
| institution | Universiti Kebangsaan Malaysia |
| language | en |
| publishDate | 2018 |
| publisher | Penerbit Universiti Kebangsaan Malaysia |
| record_format | eprints |
| spelling | my-ukm.journal.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 |
| spellingShingle | Abuasad, Salah Ishak Hashim, Homotopy decomposition method for solving higher-order time-fractional diffusion equation via modified beta derivative |
| title | 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_short | 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 |
| url | http://journalarticle.ukm.my/12672/1/33%20Salah%20Abuasad.pdf http://journalarticle.ukm.my/12672/ http://www.ukm.my/jsm/malay_journals/jilid47bil11_2018/KandunganJilid47Bil11_2018.html |
| url_provider | http://journalarticle.ukm.my/ |