An efficient technique to study of time fractional Whitham–Broer–Kaup equations
In this study, we derive the approximate analytical solution for the fractional coupled Whitham–Broer–Kaup (WBK) equations, a significant mathematical model for representing wave propagation in shallow water. The solution is obtained through the utilization of the q-homotopy analysis [Formula: see t...
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| Language: | English |
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World Scientific Publishing
2024-12-01
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| Series: | International Journal of Mathematics for Industry |
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| Online Access: | https://www.worldscientific.com/doi/10.1142/S2661335224500242 |
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| author | Nishant Bhatnagar Kanak Modi Lokesh Kumar Yadav Ravi Shanker Dubey |
| author_facet | Nishant Bhatnagar Kanak Modi Lokesh Kumar Yadav Ravi Shanker Dubey |
| author_sort | Nishant Bhatnagar |
| collection | DOAJ |
| description | In this study, we derive the approximate analytical solution for the fractional coupled Whitham–Broer–Kaup (WBK) equations, a significant mathematical model for representing wave propagation in shallow water. The solution is obtained through the utilization of the q-homotopy analysis [Formula: see text]-Laplace transform method (q-HAL[Formula: see text]TM), a hybrid approach combining [Formula: see text]-Laplace transformation and the homotopy analysis method. Homotopy polynomials are employed to address nonlinear terms, and the introduced algorithm incorporates the auxiliary parameter [Formula: see text] to regulate and fine-tune the convergence region of the resulting series solution. Comparative numerical analyses are conducted with outcomes from the Adomian decomposition method (ADM), variational iteration method (VIM), and optimal homotopy asymptotic method (OHAM), demonstrating the superior accuracy of the proposed method. The method’s novelty and straightforward implementation establish it as a reliable and efficient analytical technique for solving both linear and nonlinear fractional partial differential equations. |
| format | Article |
| id | doaj-art-13b92cbf7a1a4761b15125580828acb0 |
| institution | Kabale University |
| issn | 2661-3352 2661-3344 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | World Scientific Publishing |
| record_format | Article |
| series | International Journal of Mathematics for Industry |
| spelling | doaj-art-13b92cbf7a1a4761b15125580828acb02025-01-31T06:15:28ZengWorld Scientific PublishingInternational Journal of Mathematics for Industry2661-33522661-33442024-12-01160110.1142/S2661335224500242An efficient technique to study of time fractional Whitham–Broer–Kaup equationsNishant Bhatnagar0Kanak Modi1Lokesh Kumar Yadav2Ravi Shanker Dubey3Department of Mathematics, Amity School of Applied Sciences, Amity University Rajasthan, Jaipur, IndiaDepartment of Mathematics, Amity School of Applied Sciences, Amity University Rajasthan, Jaipur, IndiaDepartment of Mathematics, Vivekananda Global University, Jaipur, Rajasthan 303012, IndiaDepartment of Mathematics, Amity School of Applied Sciences, Amity University Rajasthan, Jaipur, IndiaIn this study, we derive the approximate analytical solution for the fractional coupled Whitham–Broer–Kaup (WBK) equations, a significant mathematical model for representing wave propagation in shallow water. The solution is obtained through the utilization of the q-homotopy analysis [Formula: see text]-Laplace transform method (q-HAL[Formula: see text]TM), a hybrid approach combining [Formula: see text]-Laplace transformation and the homotopy analysis method. Homotopy polynomials are employed to address nonlinear terms, and the introduced algorithm incorporates the auxiliary parameter [Formula: see text] to regulate and fine-tune the convergence region of the resulting series solution. Comparative numerical analyses are conducted with outcomes from the Adomian decomposition method (ADM), variational iteration method (VIM), and optimal homotopy asymptotic method (OHAM), demonstrating the superior accuracy of the proposed method. The method’s novelty and straightforward implementation establish it as a reliable and efficient analytical technique for solving both linear and nonlinear fractional partial differential equations.https://www.worldscientific.com/doi/10.1142/S2661335224500242Fractional-coupled Whitham–Broer–Kaup equationshomotopy analysis method-Laplace transformgeneralized Caputo derivative |
| spellingShingle | Nishant Bhatnagar Kanak Modi Lokesh Kumar Yadav Ravi Shanker Dubey An efficient technique to study of time fractional Whitham–Broer–Kaup equations International Journal of Mathematics for Industry Fractional-coupled Whitham–Broer–Kaup equations homotopy analysis method -Laplace transform generalized Caputo derivative |
| title | An efficient technique to study of time fractional Whitham–Broer–Kaup equations |
| title_full | An efficient technique to study of time fractional Whitham–Broer–Kaup equations |
| title_fullStr | An efficient technique to study of time fractional Whitham–Broer–Kaup equations |
| title_full_unstemmed | An efficient technique to study of time fractional Whitham–Broer–Kaup equations |
| title_short | An efficient technique to study of time fractional Whitham–Broer–Kaup equations |
| title_sort | efficient technique to study of time fractional whitham broer kaup equations |
| topic | Fractional-coupled Whitham–Broer–Kaup equations homotopy analysis method -Laplace transform generalized Caputo derivative |
| url | https://www.worldscientific.com/doi/10.1142/S2661335224500242 |
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