On solution of fractional partial differential equation by the weighted fractional operator
The motivation of this paper is to construct the solution of fractional partial differential equations (FPDEs) by the combination of Laplace transform homotopy analysis method (LHAM) and the Laplace transform residual power series method (LRPSM) with weighted Atangana-Baleanu and weighted Caputo-Fab...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Elsevier
2020-12-01
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| Series: | Alexandria Engineering Journal |
| Subjects: | |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S1110016820304312 |
| _version_ | 1818672999701676032 |
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| author | Mine Aylin Bayrak Ali Demir Ebru Ozbilge |
| author_facet | Mine Aylin Bayrak Ali Demir Ebru Ozbilge |
| author_sort | Mine Aylin Bayrak |
| collection | DOAJ |
| description | The motivation of this paper is to construct the solution of fractional partial differential equations (FPDEs) by the combination of Laplace transform homotopy analysis method (LHAM) and the Laplace transform residual power series method (LRPSM) with weighted Atangana-Baleanu and weighted Caputo-Fabrizio fractional derivatives with specific weighted functions. Moreover, the solutions are analyzed by comparing with exact solutions of these equations. The obtained consequences illustrate that methods LHAM and LRPSM work very well to determine the solutions of FPDEs with weighted fractional derivatives in consideration. |
| first_indexed | 2024-12-17T07:48:49Z |
| format | Article |
| id | doaj.art-5be44c0dfd294f2eabbb48f266281871 |
| institution | Directory Open Access Journal |
| issn | 1110-0168 |
| language | English |
| last_indexed | 2024-12-17T07:48:49Z |
| publishDate | 2020-12-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Alexandria Engineering Journal |
| spelling | doaj.art-5be44c0dfd294f2eabbb48f2662818712022-12-21T21:57:55ZengElsevierAlexandria Engineering Journal1110-01682020-12-0159648054819On solution of fractional partial differential equation by the weighted fractional operatorMine Aylin Bayrak0Ali Demir1Ebru Ozbilge2Department of Mathematics, Kocaeli University, Izmit, Kocaeli, Turkey; Corresponding author.Department of Mathematics, Kocaeli University, Izmit, Kocaeli, TurkeyDepartment of Mathematics and Statistics, American University of the Middle East, Egaila, KuwaitThe motivation of this paper is to construct the solution of fractional partial differential equations (FPDEs) by the combination of Laplace transform homotopy analysis method (LHAM) and the Laplace transform residual power series method (LRPSM) with weighted Atangana-Baleanu and weighted Caputo-Fabrizio fractional derivatives with specific weighted functions. Moreover, the solutions are analyzed by comparing with exact solutions of these equations. The obtained consequences illustrate that methods LHAM and LRPSM work very well to determine the solutions of FPDEs with weighted fractional derivatives in consideration.http://www.sciencedirect.com/science/article/pii/S1110016820304312Homotopy analysis methodResidual power series methodWeighted Atangana-Baleanu fractional derivativeWeighted Caputo-Fabrizio fractional derivativeFractional partial differential equations |
| spellingShingle | Mine Aylin Bayrak Ali Demir Ebru Ozbilge On solution of fractional partial differential equation by the weighted fractional operator Alexandria Engineering Journal Homotopy analysis method Residual power series method Weighted Atangana-Baleanu fractional derivative Weighted Caputo-Fabrizio fractional derivative Fractional partial differential equations |
| title | On solution of fractional partial differential equation by the weighted fractional operator |
| title_full | On solution of fractional partial differential equation by the weighted fractional operator |
| title_fullStr | On solution of fractional partial differential equation by the weighted fractional operator |
| title_full_unstemmed | On solution of fractional partial differential equation by the weighted fractional operator |
| title_short | On solution of fractional partial differential equation by the weighted fractional operator |
| title_sort | on solution of fractional partial differential equation by the weighted fractional operator |
| topic | Homotopy analysis method Residual power series method Weighted Atangana-Baleanu fractional derivative Weighted Caputo-Fabrizio fractional derivative Fractional partial differential equations |
| url | http://www.sciencedirect.com/science/article/pii/S1110016820304312 |
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