The generalized time-fractional Fornberg–Whitham equation: An analytic approach
This work implements a novel analytical approach known as the q-Homotopy Analysis Shehu Transform Method to the time-fractional Fornberg–Whitham equation in Caputo’s sense. The proposed method combines the idea of the q-Homotopy analysis method with the Shehu transform to enhance the efficacy of the...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Elsevier
2022-06-01
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| Series: | Partial Differential Equations in Applied Mathematics |
| Subjects: | |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S266681812200047X |
| _version_ | 1818204800904331264 |
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| author | Parthkumar P. Sartanpara Ramakanta Meher S.K. Meher |
| author_facet | Parthkumar P. Sartanpara Ramakanta Meher S.K. Meher |
| author_sort | Parthkumar P. Sartanpara |
| collection | DOAJ |
| description | This work implements a novel analytical approach known as the q-Homotopy Analysis Shehu Transform Method to the time-fractional Fornberg–Whitham equation in Caputo’s sense. The proposed method combines the idea of the q-Homotopy analysis method with the Shehu transform to enhance the efficacy of the proposed method. To demonstrate the correctness of the proposed method, the convergence analysis of the method has been obtained along with its term approximations. Finally, the obtained numerical solution is compared with the available Laplace Adomian decomposition method (LADM) solution and with the exact answer to test the efficiency of the q-HAShTM through the control parameter ħ and n. |
| first_indexed | 2024-12-12T03:47:00Z |
| format | Article |
| id | doaj.art-6f4d5df881dd4808934366068721187d |
| institution | Directory Open Access Journal |
| issn | 2666-8181 |
| language | English |
| last_indexed | 2024-12-12T03:47:00Z |
| publishDate | 2022-06-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Partial Differential Equations in Applied Mathematics |
| spelling | doaj.art-6f4d5df881dd4808934366068721187d2022-12-22T00:39:30ZengElsevierPartial Differential Equations in Applied Mathematics2666-81812022-06-015100350The generalized time-fractional Fornberg–Whitham equation: An analytic approachParthkumar P. Sartanpara0Ramakanta Meher1S.K. Meher2Department of Mathematics and Humanities, Sardar Vallabhbhai National Institute of Technology, Surat 395007, Gujarat, IndiaDepartment of Mathematics and Humanities, Sardar Vallabhbhai National Institute of Technology, Surat 395007, Gujarat, IndiaDepartment of Mathematics, Central Agricultural University, Lamphelpat, Imphal West, Manipur 795004, India; Corresponding author.This work implements a novel analytical approach known as the q-Homotopy Analysis Shehu Transform Method to the time-fractional Fornberg–Whitham equation in Caputo’s sense. The proposed method combines the idea of the q-Homotopy analysis method with the Shehu transform to enhance the efficacy of the proposed method. To demonstrate the correctness of the proposed method, the convergence analysis of the method has been obtained along with its term approximations. Finally, the obtained numerical solution is compared with the available Laplace Adomian decomposition method (LADM) solution and with the exact answer to test the efficiency of the q-HAShTM through the control parameter ħ and n.http://www.sciencedirect.com/science/article/pii/S266681812200047XTime-fractional Fornberg–Whitham equationShehu transformq-Homotopy Analysis Shehu Transform MethodCaputo fractional derivative |
| spellingShingle | Parthkumar P. Sartanpara Ramakanta Meher S.K. Meher The generalized time-fractional Fornberg–Whitham equation: An analytic approach Partial Differential Equations in Applied Mathematics Time-fractional Fornberg–Whitham equation Shehu transform q-Homotopy Analysis Shehu Transform Method Caputo fractional derivative |
| title | The generalized time-fractional Fornberg–Whitham equation: An analytic approach |
| title_full | The generalized time-fractional Fornberg–Whitham equation: An analytic approach |
| title_fullStr | The generalized time-fractional Fornberg–Whitham equation: An analytic approach |
| title_full_unstemmed | The generalized time-fractional Fornberg–Whitham equation: An analytic approach |
| title_short | The generalized time-fractional Fornberg–Whitham equation: An analytic approach |
| title_sort | generalized time fractional fornberg whitham equation an analytic approach |
| topic | Time-fractional Fornberg–Whitham equation Shehu transform q-Homotopy Analysis Shehu Transform Method Caputo fractional derivative |
| url | http://www.sciencedirect.com/science/article/pii/S266681812200047X |
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