Fractional Whitham–Broer–Kaup Equations within Modified Analytical Approaches
The fractional traveling wave solution of important Whitham−Broer−Kaup equations was investigated by using the q-homotopy analysis transform method and natural decomposition method. The Caputo definition of fractional derivatives is used to describe the fractional operator. The o...
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| Format: | Article |
| Language: | English |
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MDPI AG
2019-11-01
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| Series: | Axioms |
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| Online Access: | https://www.mdpi.com/2075-1680/8/4/125 |
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| author | Rasool Shah Hassan Khan Dumitru Baleanu |
| author_facet | Rasool Shah Hassan Khan Dumitru Baleanu |
| author_sort | Rasool Shah |
| collection | DOAJ |
| description | The fractional traveling wave solution of important Whitham−Broer−Kaup equations was investigated by using the q-homotopy analysis transform method and natural decomposition method. The Caputo definition of fractional derivatives is used to describe the fractional operator. The obtained results, using the suggested methods are compared with each other as well as with the exact results of the problems. The comparison shows the best agreement of solutions with each other and with the exact solution as well. Moreover, the proposed methods are found to be accurate, effective, and straightforward while dealing with the fractional-order system of partial differential equations and therefore can be generalized to other fractional order complex problems from engineering and science. |
| first_indexed | 2024-12-10T15:15:05Z |
| format | Article |
| id | doaj.art-23085fde44214f0f858175b7122bfe78 |
| institution | Directory Open Access Journal |
| issn | 2075-1680 |
| language | English |
| last_indexed | 2024-12-10T15:15:05Z |
| publishDate | 2019-11-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Axioms |
| spelling | doaj.art-23085fde44214f0f858175b7122bfe782022-12-22T01:43:49ZengMDPI AGAxioms2075-16802019-11-018412510.3390/axioms8040125axioms8040125Fractional Whitham–Broer–Kaup Equations within Modified Analytical ApproachesRasool Shah0Hassan Khan1Dumitru Baleanu2Department of Mathematics, Abdul Wali Khan University, Mardan 23200, PakistanDepartment of Mathematics, Abdul Wali Khan University, Mardan 23200, PakistanDepartment of Mathematics, Faculty of Arts and Sciences, Cankaya University, Ankara 06530, TurkeyThe fractional traveling wave solution of important Whitham−Broer−Kaup equations was investigated by using the q-homotopy analysis transform method and natural decomposition method. The Caputo definition of fractional derivatives is used to describe the fractional operator. The obtained results, using the suggested methods are compared with each other as well as with the exact results of the problems. The comparison shows the best agreement of solutions with each other and with the exact solution as well. Moreover, the proposed methods are found to be accurate, effective, and straightforward while dealing with the fractional-order system of partial differential equations and therefore can be generalized to other fractional order complex problems from engineering and science.https://www.mdpi.com/2075-1680/8/4/125q-homotopy analysis transform methodnatural decomposition methodwhitham–broer–kaup equationscaputo derivative |
| spellingShingle | Rasool Shah Hassan Khan Dumitru Baleanu Fractional Whitham–Broer–Kaup Equations within Modified Analytical Approaches Axioms q-homotopy analysis transform method natural decomposition method whitham–broer–kaup equations caputo derivative |
| title | Fractional Whitham–Broer–Kaup Equations within Modified Analytical Approaches |
| title_full | Fractional Whitham–Broer–Kaup Equations within Modified Analytical Approaches |
| title_fullStr | Fractional Whitham–Broer–Kaup Equations within Modified Analytical Approaches |
| title_full_unstemmed | Fractional Whitham–Broer–Kaup Equations within Modified Analytical Approaches |
| title_short | Fractional Whitham–Broer–Kaup Equations within Modified Analytical Approaches |
| title_sort | fractional whitham broer kaup equations within modified analytical approaches |
| topic | q-homotopy analysis transform method natural decomposition method whitham–broer–kaup equations caputo derivative |
| url | https://www.mdpi.com/2075-1680/8/4/125 |
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