The solution of fractional-order system of KdV equations with exponential-decay kernel
This study uses efficient techniques to evaluate a non-linear system of Korteweg–de Vries (KdV) equations with fractional Caputo Fabrizio derivative, including the modified decomposition approach and the novel iterative transform method. The system of KdV equations and the modify scheme of KdV equat...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Elsevier
2022-07-01
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| Series: | Results in Physics |
| Subjects: | |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S221137972200328X |
| _version_ | 1828335001548095488 |
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| author | Mohammad Alshammari Naveed Iqbal Wael W. Mohammed Thongchai Botmart |
| author_facet | Mohammad Alshammari Naveed Iqbal Wael W. Mohammed Thongchai Botmart |
| author_sort | Mohammad Alshammari |
| collection | DOAJ |
| description | This study uses efficient techniques to evaluate a non-linear system of Korteweg–de Vries (KdV) equations with fractional Caputo Fabrizio derivative, including the modified decomposition approach and the novel iterative transform method. The system of KdV equations and the modify scheme of KdV equations used as a model in non-linear physical processes emerging in biology, chemistry, physics and sciences are the non-linear fractional coupled systems explored in this present analysis. Approximate analytical outcomes are represented as a series with simple components, and some features revealed a proper dependency on the fractional-order derivatives’ values. An examination of convergence and uniqueness is performed. Three test cases for the analytic findings of the fractional-order KdV equations are supplied to help understand the analytical technique of both methods. Furthermore, the efficiency of the aforementioned operations, as well as the decrease in computations, allow for a larger application. It is also demonstrated that the present methodology’s conclusions are in close agreement with the precise answers. With few computations, the series result obtained using this approach has been proven to be accurate and dependable. For various fractional-order values, numerical simulations for derived solutions are described. |
| first_indexed | 2024-04-13T21:39:56Z |
| format | Article |
| id | doaj.art-7365e667584f42fbbb9c18e68dd26729 |
| institution | Directory Open Access Journal |
| issn | 2211-3797 |
| language | English |
| last_indexed | 2024-04-13T21:39:56Z |
| publishDate | 2022-07-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Results in Physics |
| spelling | doaj.art-7365e667584f42fbbb9c18e68dd267292022-12-22T02:28:48ZengElsevierResults in Physics2211-37972022-07-0138105615The solution of fractional-order system of KdV equations with exponential-decay kernelMohammad Alshammari0Naveed Iqbal1Wael W. Mohammed2Thongchai Botmart3Department of Mathematics, College of Science, University of Ha’il, Ha’il 2440, Saudi ArabiaDepartment of Mathematics, College of Science, University of Ha’il, Ha’il 2440, Saudi ArabiaDepartment of Mathematics, College of Science, University of Ha’il, Ha’il 2440, Saudi Arabia; Faculty of Science, Mansoura University, Mansoura, 35516, EgyptDepartment of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen 40002, Thailand; Corresponding author.This study uses efficient techniques to evaluate a non-linear system of Korteweg–de Vries (KdV) equations with fractional Caputo Fabrizio derivative, including the modified decomposition approach and the novel iterative transform method. The system of KdV equations and the modify scheme of KdV equations used as a model in non-linear physical processes emerging in biology, chemistry, physics and sciences are the non-linear fractional coupled systems explored in this present analysis. Approximate analytical outcomes are represented as a series with simple components, and some features revealed a proper dependency on the fractional-order derivatives’ values. An examination of convergence and uniqueness is performed. Three test cases for the analytic findings of the fractional-order KdV equations are supplied to help understand the analytical technique of both methods. Furthermore, the efficiency of the aforementioned operations, as well as the decrease in computations, allow for a larger application. It is also demonstrated that the present methodology’s conclusions are in close agreement with the precise answers. With few computations, the series result obtained using this approach has been proven to be accurate and dependable. For various fractional-order values, numerical simulations for derived solutions are described.http://www.sciencedirect.com/science/article/pii/S221137972200328XYang transformCaputo–Fabrizio derivativeSystem of Korteweg–de Vries equationsNew iterative transform methodModified decomposition method |
| spellingShingle | Mohammad Alshammari Naveed Iqbal Wael W. Mohammed Thongchai Botmart The solution of fractional-order system of KdV equations with exponential-decay kernel Results in Physics Yang transform Caputo–Fabrizio derivative System of Korteweg–de Vries equations New iterative transform method Modified decomposition method |
| title | The solution of fractional-order system of KdV equations with exponential-decay kernel |
| title_full | The solution of fractional-order system of KdV equations with exponential-decay kernel |
| title_fullStr | The solution of fractional-order system of KdV equations with exponential-decay kernel |
| title_full_unstemmed | The solution of fractional-order system of KdV equations with exponential-decay kernel |
| title_short | The solution of fractional-order system of KdV equations with exponential-decay kernel |
| title_sort | solution of fractional order system of kdv equations with exponential decay kernel |
| topic | Yang transform Caputo–Fabrizio derivative System of Korteweg–de Vries equations New iterative transform method Modified decomposition method |
| url | http://www.sciencedirect.com/science/article/pii/S221137972200328X |
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