Solution for fractional potential KdV and Benjamin equations using the novel technique
In this paper, we find the solutions for fractional potential Korteweg–de Vries (p-KdV) and Benjamin equations using q-homotopy analysis transform method(q-HATM). The considered method is the mixture of q-homotopy analysis method and Laplace transform, and the Caputo fractional operator is considere...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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Elsevier
2021-09-01
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| Series: | Journal of Ocean Engineering and Science |
| Subjects: | |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S2468013321000036 |
| _version_ | 1811227250154012672 |
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| author | P. Veeresha D.G. Prakasha N. Magesh A. John Christopher Deepak Umrao Sarwe |
| author_facet | P. Veeresha D.G. Prakasha N. Magesh A. John Christopher Deepak Umrao Sarwe |
| author_sort | P. Veeresha |
| collection | DOAJ |
| description | In this paper, we find the solutions for fractional potential Korteweg–de Vries (p-KdV) and Benjamin equations using q-homotopy analysis transform method(q-HATM). The considered method is the mixture of q-homotopy analysis method and Laplace transform, and the Caputo fractional operator is considered in the present investigation. The projected solution procedure manipulates and controls the obtained results in a large admissible domain. Further, it offers a simple algorithm to adjust the convergence province of the obtained solution. To validate the q-HATM is accurate and reliable, the numerical simulations have been conducted for both equations and the outcomes are revealed through the plots and tables. Comparison between the obtained solutions with the exact solutions exhibits that, the considered method is efficient and effective in solving nonlinear problems associated with science and technology. |
| first_indexed | 2024-04-12T09:39:27Z |
| format | Article |
| id | doaj.art-e652d9c05d6d4b259e84eba18b20592b |
| institution | Directory Open Access Journal |
| issn | 2468-0133 |
| language | English |
| last_indexed | 2024-04-12T09:39:27Z |
| publishDate | 2021-09-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Journal of Ocean Engineering and Science |
| spelling | doaj.art-e652d9c05d6d4b259e84eba18b20592b2022-12-22T03:38:08ZengElsevierJournal of Ocean Engineering and Science2468-01332021-09-0163265275Solution for fractional potential KdV and Benjamin equations using the novel techniqueP. Veeresha0D.G. Prakasha1N. Magesh2A. John Christopher3Deepak Umrao Sarwe4Department of Mathematics, CHRIST (Deemed to be University), Bengaluru-560029, IndiaDepartment of Mathematics, Faculty of Science, Davangere University, Shivagangothri, Davangere-577007, India; Corresponding author.P. G. and Research Department of Mathematics, Govt. Arts College for Men, Krishnagiri - 635 001, IndiaP. G. and Research Department of Mathematics, Govt. Arts College for Men, Krishnagiri - 635 001, IndiaDepartment of Mathematics, University of Mumbai, Kalina, Santacruz East, Mumbai-400098, IndiaIn this paper, we find the solutions for fractional potential Korteweg–de Vries (p-KdV) and Benjamin equations using q-homotopy analysis transform method(q-HATM). The considered method is the mixture of q-homotopy analysis method and Laplace transform, and the Caputo fractional operator is considered in the present investigation. The projected solution procedure manipulates and controls the obtained results in a large admissible domain. Further, it offers a simple algorithm to adjust the convergence province of the obtained solution. To validate the q-HATM is accurate and reliable, the numerical simulations have been conducted for both equations and the outcomes are revealed through the plots and tables. Comparison between the obtained solutions with the exact solutions exhibits that, the considered method is efficient and effective in solving nonlinear problems associated with science and technology.http://www.sciencedirect.com/science/article/pii/S2468013321000036Potential KdV equationq-Homotopy analysis methodFractional Benjamin equationLaplace transformGinzburg–Landau equationCaputo fractional operator |
| spellingShingle | P. Veeresha D.G. Prakasha N. Magesh A. John Christopher Deepak Umrao Sarwe Solution for fractional potential KdV and Benjamin equations using the novel technique Journal of Ocean Engineering and Science Potential KdV equation q-Homotopy analysis method Fractional Benjamin equation Laplace transform Ginzburg–Landau equation Caputo fractional operator |
| title | Solution for fractional potential KdV and Benjamin equations using the novel technique |
| title_full | Solution for fractional potential KdV and Benjamin equations using the novel technique |
| title_fullStr | Solution for fractional potential KdV and Benjamin equations using the novel technique |
| title_full_unstemmed | Solution for fractional potential KdV and Benjamin equations using the novel technique |
| title_short | Solution for fractional potential KdV and Benjamin equations using the novel technique |
| title_sort | solution for fractional potential kdv and benjamin equations using the novel technique |
| topic | Potential KdV equation q-Homotopy analysis method Fractional Benjamin equation Laplace transform Ginzburg–Landau equation Caputo fractional operator |
| url | http://www.sciencedirect.com/science/article/pii/S2468013321000036 |
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