Numerical Investigation of the Time-Fractional Whitham–Broer–Kaup Equation Involving without Singular Kernel Operators
This paper aims to implement an analytical method, known as the Laplace homotopy perturbation transform technique, for the result of fractional-order Whitham–Broer–Kaup equations. The technique is a mixture of the Laplace transformation and homotopy perturbation technique. Fractional derivatives wit...
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| Main Authors: | , , , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2021-01-01
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| Series: | Complexity |
| Online Access: | http://dx.doi.org/10.1155/2021/7979365 |
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| author | Kamsing Nonlaopon Muhammad Naeem Ahmed M. Zidan Rasool Shah Ahmed Alsanad Abdu Gumaei |
| author_facet | Kamsing Nonlaopon Muhammad Naeem Ahmed M. Zidan Rasool Shah Ahmed Alsanad Abdu Gumaei |
| author_sort | Kamsing Nonlaopon |
| collection | DOAJ |
| description | This paper aims to implement an analytical method, known as the Laplace homotopy perturbation transform technique, for the result of fractional-order Whitham–Broer–Kaup equations. The technique is a mixture of the Laplace transformation and homotopy perturbation technique. Fractional derivatives with Mittag-Leffler and exponential laws in sense of Caputo are considered. Moreover, this paper aims to show the Whitham–Broer–Kaup equations with both derivatives to see their difference in a real-world problem. The efficiency of both operators is confirmed by the outcome of the actual results of the Whitham–Broer–Kaup equations. Some problems have been presented to compare the solutions achieved with both fractional-order derivatives. |
| format | Article |
| id | doaj-art-9aa184515d0c4b06a1fc4ece1fdaff6a |
| institution | OA Journals |
| issn | 1076-2787 1099-0526 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Complexity |
| spelling | doaj-art-9aa184515d0c4b06a1fc4ece1fdaff6a2025-08-20T02:20:26ZengWileyComplexity1076-27871099-05262021-01-01202110.1155/2021/79793657979365Numerical Investigation of the Time-Fractional Whitham–Broer–Kaup Equation Involving without Singular Kernel OperatorsKamsing Nonlaopon0Muhammad Naeem1Ahmed M. Zidan2Rasool Shah3Ahmed Alsanad4Abdu Gumaei5Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen 40002, ThailandDeanship of Joint First Year Umm Al-Qura University, Makkah, Saudi ArabiaDepartment of Mathematics, College of Science, King Khalid University, Abha 9004, Saudi ArabiaDepartment of Mathematics, Abdul Wali University Mardan, Mardan, PakistanSTC’s Artificial Intelligent Chair, Department of Information Systems, College of Computer and Information Sciences, King Saud University, Riyadh 11451, Saudi ArabiaSTC’s Artificial Intelligent Chair, Department of Information Systems, College of Computer and Information Sciences, King Saud University, Riyadh 11451, Saudi ArabiaThis paper aims to implement an analytical method, known as the Laplace homotopy perturbation transform technique, for the result of fractional-order Whitham–Broer–Kaup equations. The technique is a mixture of the Laplace transformation and homotopy perturbation technique. Fractional derivatives with Mittag-Leffler and exponential laws in sense of Caputo are considered. Moreover, this paper aims to show the Whitham–Broer–Kaup equations with both derivatives to see their difference in a real-world problem. The efficiency of both operators is confirmed by the outcome of the actual results of the Whitham–Broer–Kaup equations. Some problems have been presented to compare the solutions achieved with both fractional-order derivatives.http://dx.doi.org/10.1155/2021/7979365 |
| spellingShingle | Kamsing Nonlaopon Muhammad Naeem Ahmed M. Zidan Rasool Shah Ahmed Alsanad Abdu Gumaei Numerical Investigation of the Time-Fractional Whitham–Broer–Kaup Equation Involving without Singular Kernel Operators Complexity |
| title | Numerical Investigation of the Time-Fractional Whitham–Broer–Kaup Equation Involving without Singular Kernel Operators |
| title_full | Numerical Investigation of the Time-Fractional Whitham–Broer–Kaup Equation Involving without Singular Kernel Operators |
| title_fullStr | Numerical Investigation of the Time-Fractional Whitham–Broer–Kaup Equation Involving without Singular Kernel Operators |
| title_full_unstemmed | Numerical Investigation of the Time-Fractional Whitham–Broer–Kaup Equation Involving without Singular Kernel Operators |
| title_short | Numerical Investigation of the Time-Fractional Whitham–Broer–Kaup Equation Involving without Singular Kernel Operators |
| title_sort | numerical investigation of the time fractional whitham broer kaup equation involving without singular kernel operators |
| url | http://dx.doi.org/10.1155/2021/7979365 |
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