A Comparative Analysis of the Fractional-Order Coupled Korteweg–De Vries Equations with the Mittag–Leffler Law
This article applies efficient methods, namely, modified decomposition method and new iterative transformation method, to analyze a nonlinear system of Korteweg–de Vries equations with the Atangana–Baleanu fractional derivative. The nonlinear fractional coupled systems investigated in this current a...
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| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2022-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2022/8876149 |
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| author | Noufe H. Aljahdaly Ali Akgül Rasool Shah Ibrahim Mahariq Jeevan Kafle |
| author_facet | Noufe H. Aljahdaly Ali Akgül Rasool Shah Ibrahim Mahariq Jeevan Kafle |
| author_sort | Noufe H. Aljahdaly |
| collection | DOAJ |
| description | This article applies efficient methods, namely, modified decomposition method and new iterative transformation method, to analyze a nonlinear system of Korteweg–de Vries equations with the Atangana–Baleanu fractional derivative. The nonlinear fractional coupled systems investigated in this current analysis are the system of Korteweg–de Vries and the modified system of Korteweg–de Vries equations applied as a model in nonlinear physical phenomena arising in chemistry, biology, physics, and applied sciences. Approximate analytical results are represented in the form of a series with straightforward components, and some aspects showed an appropriate dependence on the values of the fractional-order derivatives. The convergence and uniqueness analysis is carried out. To comprehend the analytical procedure of both methods, three test examples are provided for the analytical results of the time-fractional KdV equation. Additionally, the efficiency of the mentioned procedures and the reduction in calculations provide broader applicability. It is also illustrated that the findings of the current methodology are in close harmony with the exact solutions. The series result achieved applying this technique is proved to be accurate and reliable with minimal calculations. The numerical simulations for obtained solutions are discussed for different values of the fractional order. |
| format | Article |
| id | doaj-art-fa0e942f9e3a43b4922f4394efcde72a |
| institution | DOAJ |
| issn | 2314-4785 |
| language | English |
| publishDate | 2022-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-fa0e942f9e3a43b4922f4394efcde72a2025-08-20T03:20:01ZengWileyJournal of Mathematics2314-47852022-01-01202210.1155/2022/8876149A Comparative Analysis of the Fractional-Order Coupled Korteweg–De Vries Equations with the Mittag–Leffler LawNoufe H. Aljahdaly0Ali Akgül1Rasool Shah2Ibrahim Mahariq3Jeevan Kafle4Mathematics DepartmentSiirt UniversityDepartment of MathematicsCollege of Engineering and TechnologyCentral Department of MathematicsThis article applies efficient methods, namely, modified decomposition method and new iterative transformation method, to analyze a nonlinear system of Korteweg–de Vries equations with the Atangana–Baleanu fractional derivative. The nonlinear fractional coupled systems investigated in this current analysis are the system of Korteweg–de Vries and the modified system of Korteweg–de Vries equations applied as a model in nonlinear physical phenomena arising in chemistry, biology, physics, and applied sciences. Approximate analytical results are represented in the form of a series with straightforward components, and some aspects showed an appropriate dependence on the values of the fractional-order derivatives. The convergence and uniqueness analysis is carried out. To comprehend the analytical procedure of both methods, three test examples are provided for the analytical results of the time-fractional KdV equation. Additionally, the efficiency of the mentioned procedures and the reduction in calculations provide broader applicability. It is also illustrated that the findings of the current methodology are in close harmony with the exact solutions. The series result achieved applying this technique is proved to be accurate and reliable with minimal calculations. The numerical simulations for obtained solutions are discussed for different values of the fractional order.http://dx.doi.org/10.1155/2022/8876149 |
| spellingShingle | Noufe H. Aljahdaly Ali Akgül Rasool Shah Ibrahim Mahariq Jeevan Kafle A Comparative Analysis of the Fractional-Order Coupled Korteweg–De Vries Equations with the Mittag–Leffler Law Journal of Mathematics |
| title | A Comparative Analysis of the Fractional-Order Coupled Korteweg–De Vries Equations with the Mittag–Leffler Law |
| title_full | A Comparative Analysis of the Fractional-Order Coupled Korteweg–De Vries Equations with the Mittag–Leffler Law |
| title_fullStr | A Comparative Analysis of the Fractional-Order Coupled Korteweg–De Vries Equations with the Mittag–Leffler Law |
| title_full_unstemmed | A Comparative Analysis of the Fractional-Order Coupled Korteweg–De Vries Equations with the Mittag–Leffler Law |
| title_short | A Comparative Analysis of the Fractional-Order Coupled Korteweg–De Vries Equations with the Mittag–Leffler Law |
| title_sort | comparative analysis of the fractional order coupled korteweg de vries equations with the mittag leffler law |
| url | http://dx.doi.org/10.1155/2022/8876149 |
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