Approximate solution of Newell-Whitehead-Segel model with time-fractional derivative.
In the current analysis, we developed a significant approach for deriving the approximate solution of the Newell-Whitehead-Segel model with Caputo derivatives. This scheme is developed based on Sumudu transform and the residual power series method (RPSM) that generates the solution in the form of a...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Public Library of Science (PLoS)
2023-01-01
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| Series: | PLoS ONE |
| Online Access: | https://journals.plos.org/plosone/article/file?id=10.1371/journal.pone.0288740&type=printable |
| _version_ | 1797650672366125056 |
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| author | Jinxing Liu Muhammad Nadeem Yahya Alsayyad |
| author_facet | Jinxing Liu Muhammad Nadeem Yahya Alsayyad |
| author_sort | Jinxing Liu |
| collection | DOAJ |
| description | In the current analysis, we developed a significant approach for deriving the approximate solution of the Newell-Whitehead-Segel model with Caputo derivatives. This scheme is developed based on Sumudu transform and the residual power series method (RPSM) that generates the solution in the form of a series. First, we apply the Sumudu transform to decompose the fractional order and obtain a recurrence relation. Secondly, we utilize the RPSM to the recalescence relation and then we can derive the series solution with successive iterations using the initial conditions. We observe that this approach demonstrates a high accuracy and validity to the proposed fractional model. In our developed scheme, we do not face any huge calculation and restriction of elements that diverse the significance of the results. In addition, we display 2D and 3D graphical visuals to show the physical nature of the fractional model. |
| first_indexed | 2024-03-11T16:03:42Z |
| format | Article |
| id | doaj.art-137e67a77ded4e9b9938f55a8794d644 |
| institution | Directory Open Access Journal |
| issn | 1932-6203 |
| language | English |
| last_indexed | 2024-03-11T16:03:42Z |
| publishDate | 2023-01-01 |
| publisher | Public Library of Science (PLoS) |
| record_format | Article |
| series | PLoS ONE |
| spelling | doaj.art-137e67a77ded4e9b9938f55a8794d6442023-10-25T05:31:14ZengPublic Library of Science (PLoS)PLoS ONE1932-62032023-01-01187e028874010.1371/journal.pone.0288740Approximate solution of Newell-Whitehead-Segel model with time-fractional derivative.Jinxing LiuMuhammad NadeemYahya AlsayyadIn the current analysis, we developed a significant approach for deriving the approximate solution of the Newell-Whitehead-Segel model with Caputo derivatives. This scheme is developed based on Sumudu transform and the residual power series method (RPSM) that generates the solution in the form of a series. First, we apply the Sumudu transform to decompose the fractional order and obtain a recurrence relation. Secondly, we utilize the RPSM to the recalescence relation and then we can derive the series solution with successive iterations using the initial conditions. We observe that this approach demonstrates a high accuracy and validity to the proposed fractional model. In our developed scheme, we do not face any huge calculation and restriction of elements that diverse the significance of the results. In addition, we display 2D and 3D graphical visuals to show the physical nature of the fractional model.https://journals.plos.org/plosone/article/file?id=10.1371/journal.pone.0288740&type=printable |
| spellingShingle | Jinxing Liu Muhammad Nadeem Yahya Alsayyad Approximate solution of Newell-Whitehead-Segel model with time-fractional derivative. PLoS ONE |
| title | Approximate solution of Newell-Whitehead-Segel model with time-fractional derivative. |
| title_full | Approximate solution of Newell-Whitehead-Segel model with time-fractional derivative. |
| title_fullStr | Approximate solution of Newell-Whitehead-Segel model with time-fractional derivative. |
| title_full_unstemmed | Approximate solution of Newell-Whitehead-Segel model with time-fractional derivative. |
| title_short | Approximate solution of Newell-Whitehead-Segel model with time-fractional derivative. |
| title_sort | approximate solution of newell whitehead segel model with time fractional derivative |
| url | https://journals.plos.org/plosone/article/file?id=10.1371/journal.pone.0288740&type=printable |
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