On Semianalytical Study of Fractional-Order Kawahara Partial Differential Equation with the Homotopy Perturbation Method
In this study, we investigate the semianalytic solution of the fifth-order Kawahara partial differential equation (KPDE) with the approach of fractional-order derivative. We use Caputo-type derivative to investigate the said problem by using the homotopy perturbation method (HPM) for the required so...
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| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2021-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2021/6045722 |
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| author | Muhammad Sinan Kamal Shah Zareen A. Khan Qasem Al-Mdallal Fathalla Rihan |
| author_facet | Muhammad Sinan Kamal Shah Zareen A. Khan Qasem Al-Mdallal Fathalla Rihan |
| author_sort | Muhammad Sinan |
| collection | DOAJ |
| description | In this study, we investigate the semianalytic solution of the fifth-order Kawahara partial differential equation (KPDE) with the approach of fractional-order derivative. We use Caputo-type derivative to investigate the said problem by using the homotopy perturbation method (HPM) for the required solution. We obtain the solution in the form of infinite series. We next triggered different parametric effects (such as x, t, and so on) on the structure of the solitary wave propagation, demonstrating that the breadth and amplitude of the solitary wave potential may alter when these parameters are changed. We have demonstrated that He’s approach is highly effective and powerful for the solution of such a higher-order nonlinear partial differential equation through our calculations and simulations. We may apply our method to an additional complicated problem, particularly on the applied side, such as astrophysics, plasma physics, and quantum mechanics, to perform complex theoretical computation. Graphical presentation of few terms approximate solutions are given at different fractional orders. |
| format | Article |
| id | doaj-art-ca9d89d43ce54851ba80b5d4ded8a4ae |
| institution | Kabale University |
| issn | 2314-4785 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-ca9d89d43ce54851ba80b5d4ded8a4ae2025-02-03T06:06:26ZengWileyJournal of Mathematics2314-47852021-01-01202110.1155/2021/6045722On Semianalytical Study of Fractional-Order Kawahara Partial Differential Equation with the Homotopy Perturbation MethodMuhammad Sinan0Kamal Shah1Zareen A. Khan2Qasem Al-Mdallal3Fathalla Rihan4School of Mathematical SciencesDepartment of MathematicsCollege of ScienceDepartment of Mathematical SciencesDepartment of Mathematical SciencesIn this study, we investigate the semianalytic solution of the fifth-order Kawahara partial differential equation (KPDE) with the approach of fractional-order derivative. We use Caputo-type derivative to investigate the said problem by using the homotopy perturbation method (HPM) for the required solution. We obtain the solution in the form of infinite series. We next triggered different parametric effects (such as x, t, and so on) on the structure of the solitary wave propagation, demonstrating that the breadth and amplitude of the solitary wave potential may alter when these parameters are changed. We have demonstrated that He’s approach is highly effective and powerful for the solution of such a higher-order nonlinear partial differential equation through our calculations and simulations. We may apply our method to an additional complicated problem, particularly on the applied side, such as astrophysics, plasma physics, and quantum mechanics, to perform complex theoretical computation. Graphical presentation of few terms approximate solutions are given at different fractional orders.http://dx.doi.org/10.1155/2021/6045722 |
| spellingShingle | Muhammad Sinan Kamal Shah Zareen A. Khan Qasem Al-Mdallal Fathalla Rihan On Semianalytical Study of Fractional-Order Kawahara Partial Differential Equation with the Homotopy Perturbation Method Journal of Mathematics |
| title | On Semianalytical Study of Fractional-Order Kawahara Partial Differential Equation with the Homotopy Perturbation Method |
| title_full | On Semianalytical Study of Fractional-Order Kawahara Partial Differential Equation with the Homotopy Perturbation Method |
| title_fullStr | On Semianalytical Study of Fractional-Order Kawahara Partial Differential Equation with the Homotopy Perturbation Method |
| title_full_unstemmed | On Semianalytical Study of Fractional-Order Kawahara Partial Differential Equation with the Homotopy Perturbation Method |
| title_short | On Semianalytical Study of Fractional-Order Kawahara Partial Differential Equation with the Homotopy Perturbation Method |
| title_sort | on semianalytical study of fractional order kawahara partial differential equation with the homotopy perturbation method |
| url | http://dx.doi.org/10.1155/2021/6045722 |
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