New homotopy analysis transform method for solving multidimensional fractional diffusion equations
In this paper, we introduce a new semi-analytical method called the homotopy analysis Shehu transform method (HASTM) for solving multidimensional fractional diffusion equations. The proposed technique is a combination of the homotopy analysis method and the Laplace-type integral transform called the...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Taylor & Francis Group
2020-01-01
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| Series: | Arab Journal of Basic and Applied Sciences |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1080/25765299.2019.1706234 |
| _version_ | 1818662147429761024 |
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| author | Shehu Maitama Weidong Zhao |
| author_facet | Shehu Maitama Weidong Zhao |
| author_sort | Shehu Maitama |
| collection | DOAJ |
| description | In this paper, we introduce a new semi-analytical method called the homotopy analysis Shehu transform method (HASTM) for solving multidimensional fractional diffusion equations. The proposed technique is a combination of the homotopy analysis method and the Laplace-type integral transform called the Shehu transform which is a generalization of the Laplace and the Sumudu integral transforms. Shehu transform is user-friendly, and its visualization is easier than the Sumudu, and the natural transforms. The convergence analysis of the method is proved, and we provide some applications of the fractional diffusion equations to validate the efficiency and the high accuracy of the technique. The results obtained using the HASTM are in complete agreement with the results of the existing techniques. |
| first_indexed | 2024-12-17T04:56:20Z |
| format | Article |
| id | doaj.art-7189e676dcba42a183476b9ea76092d7 |
| institution | Directory Open Access Journal |
| issn | 2576-5299 |
| language | English |
| last_indexed | 2024-12-17T04:56:20Z |
| publishDate | 2020-01-01 |
| publisher | Taylor & Francis Group |
| record_format | Article |
| series | Arab Journal of Basic and Applied Sciences |
| spelling | doaj.art-7189e676dcba42a183476b9ea76092d72022-12-21T22:02:41ZengTaylor & Francis GroupArab Journal of Basic and Applied Sciences2576-52992020-01-01271274410.1080/25765299.2019.17062341706234New homotopy analysis transform method for solving multidimensional fractional diffusion equationsShehu Maitama0Weidong Zhao1School of Mathematics, Shandong UniversitySchool of Mathematics, Shandong UniversityIn this paper, we introduce a new semi-analytical method called the homotopy analysis Shehu transform method (HASTM) for solving multidimensional fractional diffusion equations. The proposed technique is a combination of the homotopy analysis method and the Laplace-type integral transform called the Shehu transform which is a generalization of the Laplace and the Sumudu integral transforms. Shehu transform is user-friendly, and its visualization is easier than the Sumudu, and the natural transforms. The convergence analysis of the method is proved, and we provide some applications of the fractional diffusion equations to validate the efficiency and the high accuracy of the technique. The results obtained using the HASTM are in complete agreement with the results of the existing techniques.http://dx.doi.org/10.1080/25765299.2019.1706234shehu transform methodhomotopy analysis shehu transform methodfractional diffusion equationssymbolic-numeric computation |
| spellingShingle | Shehu Maitama Weidong Zhao New homotopy analysis transform method for solving multidimensional fractional diffusion equations Arab Journal of Basic and Applied Sciences shehu transform method homotopy analysis shehu transform method fractional diffusion equations symbolic-numeric computation |
| title | New homotopy analysis transform method for solving multidimensional fractional diffusion equations |
| title_full | New homotopy analysis transform method for solving multidimensional fractional diffusion equations |
| title_fullStr | New homotopy analysis transform method for solving multidimensional fractional diffusion equations |
| title_full_unstemmed | New homotopy analysis transform method for solving multidimensional fractional diffusion equations |
| title_short | New homotopy analysis transform method for solving multidimensional fractional diffusion equations |
| title_sort | new homotopy analysis transform method for solving multidimensional fractional diffusion equations |
| topic | shehu transform method homotopy analysis shehu transform method fractional diffusion equations symbolic-numeric computation |
| url | http://dx.doi.org/10.1080/25765299.2019.1706234 |
| work_keys_str_mv | AT shehumaitama newhomotopyanalysistransformmethodforsolvingmultidimensionalfractionaldiffusionequations AT weidongzhao newhomotopyanalysistransformmethodforsolvingmultidimensionalfractionaldiffusionequations |