Quadrature Solution for Fractional Benjamin–Bona–Mahony–Burger Equations
In this work, we present various novelty methods by employing the fractional differential quadrature technique to solve the time and space fractional nonlinear Benjamin–Bona–Mahony equation and the Benjamin–Bona–Mahony–Burger equation. The novelty of these methods is based on the generalized Caputo...
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| Format: | Article |
| Language: | English |
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MDPI AG
2024-11-01
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| Series: | Fractal and Fractional |
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| Online Access: | https://www.mdpi.com/2504-3110/8/12/685 |
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| author | Waleed Mohammed Abdelfattah Ola Ragb Mokhtar Mohamed Mohamed Salah Abdelfattah Mustafa |
| author_facet | Waleed Mohammed Abdelfattah Ola Ragb Mokhtar Mohamed Mohamed Salah Abdelfattah Mustafa |
| author_sort | Waleed Mohammed Abdelfattah |
| collection | DOAJ |
| description | In this work, we present various novelty methods by employing the fractional differential quadrature technique to solve the time and space fractional nonlinear Benjamin–Bona–Mahony equation and the Benjamin–Bona–Mahony–Burger equation. The novelty of these methods is based on the generalized Caputo sense, classical differential quadrature method, and discrete singular convolution methods based on two different kernels. Also, the solution strategy is to apply perturbation analysis or an iterative method to reduce the problem to a series of linear initial boundary value problems. Consequently, we apply these suggested techniques to reduce the nonlinear fractional PDEs into ordinary differential equations. Hence, to validate the suggested techniques, a solution to this problem was obtained by designing a MATLAB code for each method. Also, we compare this solution with the exact ones. Furthermore, more figures and tables have been investigated to illustrate the high accuracy and rapid convergence of these novel techniques. From the obtained solutions, it was found that the suggested techniques are easily applicable and effective, which can help in the study of the other higher-D nonlinear fractional PDEs emerging in mathematical physics. |
| format | Article |
| id | doaj-art-4247eeb7153d4088a9f9c90ee4f13317 |
| institution | Kabale University |
| issn | 2504-3110 |
| language | English |
| publishDate | 2024-11-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fractal and Fractional |
| spelling | doaj-art-4247eeb7153d4088a9f9c90ee4f133172024-12-27T14:27:00ZengMDPI AGFractal and Fractional2504-31102024-11-0181268510.3390/fractalfract8120685Quadrature Solution for Fractional Benjamin–Bona–Mahony–Burger EquationsWaleed Mohammed Abdelfattah0Ola Ragb1Mokhtar Mohamed2Mohamed Salah3Abdelfattah Mustafa4College of Engineering, University of Business and Technology, Jeddah 23435, Saudi ArabiaDepartment of Engineering Mathematics and Physics, Faculty of Engineering, Zagazig University, Zagazig 44519, EgyptBasic Science Department, Faculty of Engineering, Delta University for Science and Technology, Gamasa 11152, EgyptDepartment of Engineering Mathematics and Physics, Faculty of Engineering, Zagazig University, Zagazig 44519, EgyptDepartment of Mathematics, Faculty of Science, Islamic University of Madinah, Madinah 42351, Saudi ArabiaIn this work, we present various novelty methods by employing the fractional differential quadrature technique to solve the time and space fractional nonlinear Benjamin–Bona–Mahony equation and the Benjamin–Bona–Mahony–Burger equation. The novelty of these methods is based on the generalized Caputo sense, classical differential quadrature method, and discrete singular convolution methods based on two different kernels. Also, the solution strategy is to apply perturbation analysis or an iterative method to reduce the problem to a series of linear initial boundary value problems. Consequently, we apply these suggested techniques to reduce the nonlinear fractional PDEs into ordinary differential equations. Hence, to validate the suggested techniques, a solution to this problem was obtained by designing a MATLAB code for each method. Also, we compare this solution with the exact ones. Furthermore, more figures and tables have been investigated to illustrate the high accuracy and rapid convergence of these novel techniques. From the obtained solutions, it was found that the suggested techniques are easily applicable and effective, which can help in the study of the other higher-D nonlinear fractional PDEs emerging in mathematical physics.https://www.mdpi.com/2504-3110/8/12/685generalized Caputoquadrature approachdiscrete singular convolutionperturbation methodfractional nonlinear PDEsBenjamin–Bona–Mahony–Burger equation |
| spellingShingle | Waleed Mohammed Abdelfattah Ola Ragb Mokhtar Mohamed Mohamed Salah Abdelfattah Mustafa Quadrature Solution for Fractional Benjamin–Bona–Mahony–Burger Equations Fractal and Fractional generalized Caputo quadrature approach discrete singular convolution perturbation method fractional nonlinear PDEs Benjamin–Bona–Mahony–Burger equation |
| title | Quadrature Solution for Fractional Benjamin–Bona–Mahony–Burger Equations |
| title_full | Quadrature Solution for Fractional Benjamin–Bona–Mahony–Burger Equations |
| title_fullStr | Quadrature Solution for Fractional Benjamin–Bona–Mahony–Burger Equations |
| title_full_unstemmed | Quadrature Solution for Fractional Benjamin–Bona–Mahony–Burger Equations |
| title_short | Quadrature Solution for Fractional Benjamin–Bona–Mahony–Burger Equations |
| title_sort | quadrature solution for fractional benjamin bona mahony burger equations |
| topic | generalized Caputo quadrature approach discrete singular convolution perturbation method fractional nonlinear PDEs Benjamin–Bona–Mahony–Burger equation |
| url | https://www.mdpi.com/2504-3110/8/12/685 |
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