Optimum Solutions of Fractional Order Zakharov–Kuznetsov Equations
In this paper, the Optimal Homotopy Asymptotic Method is extended to derive the approximate solutions of fractional order two-dimensional partial differential equations. The fractional order Zakharov–Kuznetsov equation is solved as a test example, while the time fractional derivatives are described...
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| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2019-01-01
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| Series: | Complexity |
| Online Access: | http://dx.doi.org/10.1155/2019/1741958 |
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| _version_ | 1849435359251791872 |
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| author | Rashid Nawaz Laiq Zada Abraiz Khattak Muhammad Jibran Adam Khan |
| author_facet | Rashid Nawaz Laiq Zada Abraiz Khattak Muhammad Jibran Adam Khan |
| author_sort | Rashid Nawaz |
| collection | DOAJ |
| description | In this paper, the Optimal Homotopy Asymptotic Method is extended to derive the approximate solutions of fractional order two-dimensional partial differential equations. The fractional order Zakharov–Kuznetsov equation is solved as a test example, while the time fractional derivatives are described in the Caputo sense. The solutions of the problem are computed in the form of rapidly convergent series with easily calculable components using Mathematica. Reliability of the proposed method is given by comparison with other methods in the literature. The obtained results showed that the method is powerful and efficient for determination of solution of higher-dimensional fractional order partial differential equations. |
| format | Article |
| id | doaj-art-e558f61c2f9740aead60dad8d371b918 |
| institution | Kabale University |
| issn | 1076-2787 1099-0526 |
| language | English |
| publishDate | 2019-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Complexity |
| spelling | doaj-art-e558f61c2f9740aead60dad8d371b9182025-08-20T03:26:20ZengWileyComplexity1076-27871099-05262019-01-01201910.1155/2019/17419581741958Optimum Solutions of Fractional Order Zakharov–Kuznetsov EquationsRashid Nawaz0Laiq Zada1Abraiz Khattak2Muhammad Jibran3Adam Khan4Department of Mathematics, Abdul Wali Khan University Mardan, Mardan, Khaber Pakhtunkhwa, PakistanDepartment of Mathematics, Abdul Wali Khan University Mardan, Mardan, Khaber Pakhtunkhwa, PakistanDepartment of Electrical Power Engineering, U.S. Pakistan Center for Advanced Studies in Energy, National University of Sciences and Technology (NUST), Islamabad, PakistanDepartment of Computer Science and IT, Sarhad University of Science and Information Technology, Peshawar, Khaber Pakhtunkhwa, PakistanDepartment for Management of Science and Technology Development, Ton Duc Thang University, Ho Chi Minh City, VietnamIn this paper, the Optimal Homotopy Asymptotic Method is extended to derive the approximate solutions of fractional order two-dimensional partial differential equations. The fractional order Zakharov–Kuznetsov equation is solved as a test example, while the time fractional derivatives are described in the Caputo sense. The solutions of the problem are computed in the form of rapidly convergent series with easily calculable components using Mathematica. Reliability of the proposed method is given by comparison with other methods in the literature. The obtained results showed that the method is powerful and efficient for determination of solution of higher-dimensional fractional order partial differential equations.http://dx.doi.org/10.1155/2019/1741958 |
| spellingShingle | Rashid Nawaz Laiq Zada Abraiz Khattak Muhammad Jibran Adam Khan Optimum Solutions of Fractional Order Zakharov–Kuznetsov Equations Complexity |
| title | Optimum Solutions of Fractional Order Zakharov–Kuznetsov Equations |
| title_full | Optimum Solutions of Fractional Order Zakharov–Kuznetsov Equations |
| title_fullStr | Optimum Solutions of Fractional Order Zakharov–Kuznetsov Equations |
| title_full_unstemmed | Optimum Solutions of Fractional Order Zakharov–Kuznetsov Equations |
| title_short | Optimum Solutions of Fractional Order Zakharov–Kuznetsov Equations |
| title_sort | optimum solutions of fractional order zakharov kuznetsov equations |
| url | http://dx.doi.org/10.1155/2019/1741958 |
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