An efficient computational technique for time-fractional modified Degasperis-Procesi equation arising in propagation of nonlinear dispersive waves
In this paper, an efficient hybrid numerical scheme which is based on a joint venture of the q-homotopy analysis method and Sumudu transform is applied to investigate the time-fractional modified Degasperis-Procesi (DP) equation. The present study considers the Caputo fractional derivative. The frac...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Elsevier
2021-03-01
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| Series: | Journal of Ocean Engineering and Science |
| Subjects: | |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S2468013320300486 |
| _version_ | 1828823260918185984 |
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| author | Ved Prakash Dubey Rajnesh Kumar Jagdev Singh Devendra Kumar |
| author_facet | Ved Prakash Dubey Rajnesh Kumar Jagdev Singh Devendra Kumar |
| author_sort | Ved Prakash Dubey |
| collection | DOAJ |
| description | In this paper, an efficient hybrid numerical scheme which is based on a joint venture of the q-homotopy analysis method and Sumudu transform is applied to investigate the time-fractional modified Degasperis-Procesi (DP) equation. The present study considers the Caputo fractional derivative. The fractional order modified DP model is very important and plays a great role in study of ocean engineering and science. The proposed scheme provides a beautiful opportunity for proper selection of the auxiliary parameter ℏ and the asymptotic parameter ρ ( ≥ 1) to handle mainly the differential equations of nonlinear nature. The offered scheme produces the solution in the shape of a convergent series in a large admissible domain which is helpful to regulate the region of convergence of a series solution. The proposed work computes the approximate analytical solution of the fractional modified DP equation systematically and also presents graphically the variation of the obtained solution for diverse values of the fractional parameter β. |
| first_indexed | 2024-12-12T13:31:39Z |
| format | Article |
| id | doaj.art-27ffe42bb7a84a2888fe87c703b6a8c4 |
| institution | Directory Open Access Journal |
| issn | 2468-0133 |
| language | English |
| last_indexed | 2024-12-12T13:31:39Z |
| publishDate | 2021-03-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Journal of Ocean Engineering and Science |
| spelling | doaj.art-27ffe42bb7a84a2888fe87c703b6a8c42022-12-22T00:23:02ZengElsevierJournal of Ocean Engineering and Science2468-01332021-03-01613039An efficient computational technique for time-fractional modified Degasperis-Procesi equation arising in propagation of nonlinear dispersive wavesVed Prakash Dubey0Rajnesh Kumar1Jagdev Singh2Devendra Kumar3Faculty of Mathematical and Statistical Sciences, Shri Ramswaroop Memorial University, Lucknow- Deva Road, Uttar Pradesh-225003, IndiaDepartment of Applied Science and Humanities, Government Engineering College, Nawada, Department of Science and Technology, Bihar-805122, IndiaDepartment of Mathematics, JECRC University, Jaipur-303905, Rajasthan, IndiaDepartment of Mathematics, University of Rajasthan, Jaipur-302004, Rajasthan, India; Corresponding author.In this paper, an efficient hybrid numerical scheme which is based on a joint venture of the q-homotopy analysis method and Sumudu transform is applied to investigate the time-fractional modified Degasperis-Procesi (DP) equation. The present study considers the Caputo fractional derivative. The fractional order modified DP model is very important and plays a great role in study of ocean engineering and science. The proposed scheme provides a beautiful opportunity for proper selection of the auxiliary parameter ℏ and the asymptotic parameter ρ ( ≥ 1) to handle mainly the differential equations of nonlinear nature. The offered scheme produces the solution in the shape of a convergent series in a large admissible domain which is helpful to regulate the region of convergence of a series solution. The proposed work computes the approximate analytical solution of the fractional modified DP equation systematically and also presents graphically the variation of the obtained solution for diverse values of the fractional parameter β.http://www.sciencedirect.com/science/article/pii/S2468013320300486Fractional Degasperis-Procesi equationNonlinear dispersive wavesAnalytical solutionq-homotopy analysis methodSumudu transform |
| spellingShingle | Ved Prakash Dubey Rajnesh Kumar Jagdev Singh Devendra Kumar An efficient computational technique for time-fractional modified Degasperis-Procesi equation arising in propagation of nonlinear dispersive waves Journal of Ocean Engineering and Science Fractional Degasperis-Procesi equation Nonlinear dispersive waves Analytical solution q-homotopy analysis method Sumudu transform |
| title | An efficient computational technique for time-fractional modified Degasperis-Procesi equation arising in propagation of nonlinear dispersive waves |
| title_full | An efficient computational technique for time-fractional modified Degasperis-Procesi equation arising in propagation of nonlinear dispersive waves |
| title_fullStr | An efficient computational technique for time-fractional modified Degasperis-Procesi equation arising in propagation of nonlinear dispersive waves |
| title_full_unstemmed | An efficient computational technique for time-fractional modified Degasperis-Procesi equation arising in propagation of nonlinear dispersive waves |
| title_short | An efficient computational technique for time-fractional modified Degasperis-Procesi equation arising in propagation of nonlinear dispersive waves |
| title_sort | efficient computational technique for time fractional modified degasperis procesi equation arising in propagation of nonlinear dispersive waves |
| topic | Fractional Degasperis-Procesi equation Nonlinear dispersive waves Analytical solution q-homotopy analysis method Sumudu transform |
| url | http://www.sciencedirect.com/science/article/pii/S2468013320300486 |
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