Study of fractional forced KdV equation with Caputo–Fabrizio and Atangana–Baleanu–Caputo differential operators
It is essential for mathematicians, physicists, and engineers to construct fractional mathematical models for specific phenomena and develop numerical or analytical solutions for these models. In this work, we implement the natural decomposition approach with nonsingular kernel derivatives to invest...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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AIP Publishing LLC
2024-01-01
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| Series: | AIP Advances |
| Online Access: | http://dx.doi.org/10.1063/5.0185670 |
| _version_ | 1797331985789616128 |
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| author | Mashael M. AlBaidani Fahad Aljuaydi N. S. Alharthi Adnan Khan Abdul Hamid Ganie |
| author_facet | Mashael M. AlBaidani Fahad Aljuaydi N. S. Alharthi Adnan Khan Abdul Hamid Ganie |
| author_sort | Mashael M. AlBaidani |
| collection | DOAJ |
| description | It is essential for mathematicians, physicists, and engineers to construct fractional mathematical models for specific phenomena and develop numerical or analytical solutions for these models. In this work, we implement the natural decomposition approach with nonsingular kernel derivatives to investigate the solution of nonlinear fractional forced Korteweg–de Vries (FF-KdV) equation. We first investigate the FF-KdV equation under the Caputo–Fabrizio fractional derivative. The similar equations are then examined using the Atangana–Baleanu derivative. This approach combines the decomposition method with the Natural transform method. The series solution of the suggested equations is thus obtained using the natural transform. The key benefit of this novel approximate-analytical approach is that it may provide an analytical solution for the FF-KdV problem in the form of convergent series with simple computations. For each equation, three unique situations are chosen to demonstrate and test the viability of the proposed method. To guarantee the competence and dependability of the proposed method, the nature for various values of the Froude number Fr have been provided. The present approach is also used to calculate solutions at various fractional orders. The approximate series solution’s behavior for various fractional orders has been graphically displayed. The outcomes demonstrate that the methodology is simple to use and reliable when applied to numerous fractional differential equations. |
| first_indexed | 2024-03-08T07:43:04Z |
| format | Article |
| id | doaj.art-92cd4fb68b5a4df4a7cb8c59388ea763 |
| institution | Directory Open Access Journal |
| issn | 2158-3226 |
| language | English |
| last_indexed | 2024-03-08T07:43:04Z |
| publishDate | 2024-01-01 |
| publisher | AIP Publishing LLC |
| record_format | Article |
| series | AIP Advances |
| spelling | doaj.art-92cd4fb68b5a4df4a7cb8c59388ea7632024-02-02T16:46:07ZengAIP Publishing LLCAIP Advances2158-32262024-01-01141015340015340-1210.1063/5.0185670Study of fractional forced KdV equation with Caputo–Fabrizio and Atangana–Baleanu–Caputo differential operatorsMashael M. AlBaidani0Fahad Aljuaydi1N. S. Alharthi2Adnan Khan3Abdul Hamid Ganie4Department of Mathematics, College of Science and Humanities, Prince Sattam Bin Abdulaziz University, Al Kharj 11942, Saudi ArabiaDepartment of Mathematics, College of Science and Humanities, Prince Sattam Bin Abdulaziz University, Al Kharj 11942, Saudi ArabiaDepartment of Matrhematics, Faculty of Science and Arts, King Abdulaziz University, Rabigh 21911, Saudi ArabiaDepartment of Mathematics, Abdul Wali Khan University Mardan, Mardan 23200, PakistanBasic Science Department, College of Science and Theoretical Studies, Saudi Electronic University, Riyadh 11673, Saudi ArabiaIt is essential for mathematicians, physicists, and engineers to construct fractional mathematical models for specific phenomena and develop numerical or analytical solutions for these models. In this work, we implement the natural decomposition approach with nonsingular kernel derivatives to investigate the solution of nonlinear fractional forced Korteweg–de Vries (FF-KdV) equation. We first investigate the FF-KdV equation under the Caputo–Fabrizio fractional derivative. The similar equations are then examined using the Atangana–Baleanu derivative. This approach combines the decomposition method with the Natural transform method. The series solution of the suggested equations is thus obtained using the natural transform. The key benefit of this novel approximate-analytical approach is that it may provide an analytical solution for the FF-KdV problem in the form of convergent series with simple computations. For each equation, three unique situations are chosen to demonstrate and test the viability of the proposed method. To guarantee the competence and dependability of the proposed method, the nature for various values of the Froude number Fr have been provided. The present approach is also used to calculate solutions at various fractional orders. The approximate series solution’s behavior for various fractional orders has been graphically displayed. The outcomes demonstrate that the methodology is simple to use and reliable when applied to numerous fractional differential equations.http://dx.doi.org/10.1063/5.0185670 |
| spellingShingle | Mashael M. AlBaidani Fahad Aljuaydi N. S. Alharthi Adnan Khan Abdul Hamid Ganie Study of fractional forced KdV equation with Caputo–Fabrizio and Atangana–Baleanu–Caputo differential operators AIP Advances |
| title | Study of fractional forced KdV equation with Caputo–Fabrizio and Atangana–Baleanu–Caputo differential operators |
| title_full | Study of fractional forced KdV equation with Caputo–Fabrizio and Atangana–Baleanu–Caputo differential operators |
| title_fullStr | Study of fractional forced KdV equation with Caputo–Fabrizio and Atangana–Baleanu–Caputo differential operators |
| title_full_unstemmed | Study of fractional forced KdV equation with Caputo–Fabrizio and Atangana–Baleanu–Caputo differential operators |
| title_short | Study of fractional forced KdV equation with Caputo–Fabrizio and Atangana–Baleanu–Caputo differential operators |
| title_sort | study of fractional forced kdv equation with caputo fabrizio and atangana baleanu caputo differential operators |
| url | http://dx.doi.org/10.1063/5.0185670 |
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