Extension of the Optimal Auxiliary Function Method to Solve the System of a Fractional-Order Whitham–Broer–Kaup Equation
In this paper, we introduce and implement the optimal auxiliary function method to solve a system of fractional-order Whitham–Broer–Kaup equations, a class of nonlinear partial differential equations with broad applications in mathematical physics. This method provides a systematic and efficient app...
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| Published in | Fractal and fractional Vol. 8; no. 1; p. 1 |
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| Main Authors | , , , , , , |
| Format | Journal Article |
| Language | English |
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MDPI AG
01.01.2024
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| Online Access | Get full text |
| ISSN | 2504-3110 2504-3110 |
| DOI | 10.3390/fractalfract8010001 |
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| Abstract | In this paper, we introduce and implement the optimal auxiliary function method to solve a system of fractional-order Whitham–Broer–Kaup equations, a class of nonlinear partial differential equations with broad applications in mathematical physics. This method provides a systematic and efficient approach to finding accurate solutions for complex systems of fractional-order equations. We give a full analysis using tables and figures to demonstrate the reliability and accuracy of our approach. We confirm the effectiveness of our suggested method in solving the considered equations using numerical simulations and comparisons, emphasizing its potential for applications in a variety of scientific and engineering areas. |
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| AbstractList | In this paper, we introduce and implement the optimal auxiliary function method to solve a system of fractional-order Whitham–Broer–Kaup equations, a class of nonlinear partial differential equations with broad applications in mathematical physics. This method provides a systematic and efficient approach to finding accurate solutions for complex systems of fractional-order equations. We give a full analysis using tables and figures to demonstrate the reliability and accuracy of our approach. We confirm the effectiveness of our suggested method in solving the considered equations using numerical simulations and comparisons, emphasizing its potential for applications in a variety of scientific and engineering areas. |
| Audience | Academic |
| Author | Moaddy, Khaled Alshammari, Saleh Alshammari, Mohammad Al-Sawalha, M. Mossa Alderremy, Aisha Abdullah Alsheekhhussain, Zainab Shah, Rasool |
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| Cites_doi | 10.1002/mma.3962 10.1016/j.jmaa.2008.04.007 10.1016/j.eswa.2023.121292 10.1016/j.chaos.2006.05.019 10.1016/S0375-9601(01)00333-4 10.3934/math.20221031 10.3390/sym14061102 10.1016/j.camwa.2009.03.030 10.3390/math10101643 10.1155/2021/2567927 10.1016/j.physleta.2009.05.026 10.2977/prims/1195183298 10.1155/2022/7488996 10.1007/978-0-387-21746-8 10.1016/j.camwa.2013.02.003 10.1007/s10483-020-2683-7 10.2298/TSCI170612269D 10.1016/j.chaos.2021.110877 10.1016/j.bspc.2007.07.013 10.1016/j.jde.2015.08.040 10.1002/cpa.3160270108 10.3390/e17096519 10.1016/j.aej.2017.04.012 10.1155/2021/7979365 10.3390/sym14071321 10.3390/sym13050784 10.1007/s11071-010-9724-4 10.3390/sym14071463 10.3390/fractalfract7070512 10.3390/e14040701 10.2298/TSCI170804283B 10.2298/TSCI121124216Y 10.1002/zamm.19950750820 10.1007/BF02457745 10.3390/axioms8040125 10.1111/j.1365-246X.1967.tb02303.x |
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| SubjectTerms | Approximation Calculus Caputo operator Complex systems Differential equations Engineering Entropy fractional-order Whitham–Broer–Kaup equation Methods Nonlinear differential equations Nonlinear equations Numerical analysis optimal auxiliary function method Partial differential equations Physics |
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| Title | Extension of the Optimal Auxiliary Function Method to Solve the System of a Fractional-Order Whitham–Broer–Kaup Equation |
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