Analytical Approximate Solutions of Caputo Fractional KdV-Burgers Equations Using Laplace Residual Power Series Technique
The KdV-Burgers equation is one of the most important partial differential equations, established by Korteweg and de Vries to describe the behavior of nonlinear waves and many physical phenomena. In this paper, we reformulate this problem in the sense of Caputo fractional derivative, whose physical...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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Hindawi Limited
2024-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2024/7835548 |
| _version_ | 1797260567655743488 |
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| author | Aliaa Burqan Mona Khandaqji Zeyad Al-Zhour Ahmad El-Ajou Tasneem Alrahamneh |
| author_facet | Aliaa Burqan Mona Khandaqji Zeyad Al-Zhour Ahmad El-Ajou Tasneem Alrahamneh |
| author_sort | Aliaa Burqan |
| collection | DOAJ |
| description | The KdV-Burgers equation is one of the most important partial differential equations, established by Korteweg and de Vries to describe the behavior of nonlinear waves and many physical phenomena. In this paper, we reformulate this problem in the sense of Caputo fractional derivative, whose physical meanings, in this case, are very evident by describing the whole time domain of physical processing. The main aim of this work is to present the analytical approximate series for the nonlinear Caputo fractional KdV-Burgers equation by applying the Laplace residual power series method. The main tools of this method are the Laplace transform, Laurent series, and residual function. Moreover, four attractive and satisfying applications are given and solved to elucidate the mechanism of our proposed method. The analytical approximate series solution via this sweet technique shows excellent agreement with the solution obtained from other methods in simple and understandable steps. Finally, graphical and numerical comparison results at different values of α are provided with residual and relative errors to illustrate the behaviors of the approximate results and the effectiveness of the proposed method. |
| first_indexed | 2024-04-24T23:27:23Z |
| format | Article |
| id | doaj.art-aba8d6500625483dbf4fa7d0408e81c9 |
| institution | Directory Open Access Journal |
| issn | 1687-0042 |
| language | English |
| last_indexed | 2024-04-24T23:27:23Z |
| publishDate | 2024-01-01 |
| publisher | Hindawi Limited |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj.art-aba8d6500625483dbf4fa7d0408e81c92024-03-16T00:00:03ZengHindawi LimitedJournal of Applied Mathematics1687-00422024-01-01202410.1155/2024/7835548Analytical Approximate Solutions of Caputo Fractional KdV-Burgers Equations Using Laplace Residual Power Series TechniqueAliaa Burqan0Mona Khandaqji1Zeyad Al-Zhour2Ahmad El-Ajou3Tasneem Alrahamneh4Department of MathematicsDepartment of MathematicsDepartment of Basic Engineering SciencesDepartment of MathematicsDepartment of MathematicsThe KdV-Burgers equation is one of the most important partial differential equations, established by Korteweg and de Vries to describe the behavior of nonlinear waves and many physical phenomena. In this paper, we reformulate this problem in the sense of Caputo fractional derivative, whose physical meanings, in this case, are very evident by describing the whole time domain of physical processing. The main aim of this work is to present the analytical approximate series for the nonlinear Caputo fractional KdV-Burgers equation by applying the Laplace residual power series method. The main tools of this method are the Laplace transform, Laurent series, and residual function. Moreover, four attractive and satisfying applications are given and solved to elucidate the mechanism of our proposed method. The analytical approximate series solution via this sweet technique shows excellent agreement with the solution obtained from other methods in simple and understandable steps. Finally, graphical and numerical comparison results at different values of α are provided with residual and relative errors to illustrate the behaviors of the approximate results and the effectiveness of the proposed method.http://dx.doi.org/10.1155/2024/7835548 |
| spellingShingle | Aliaa Burqan Mona Khandaqji Zeyad Al-Zhour Ahmad El-Ajou Tasneem Alrahamneh Analytical Approximate Solutions of Caputo Fractional KdV-Burgers Equations Using Laplace Residual Power Series Technique Journal of Applied Mathematics |
| title | Analytical Approximate Solutions of Caputo Fractional KdV-Burgers Equations Using Laplace Residual Power Series Technique |
| title_full | Analytical Approximate Solutions of Caputo Fractional KdV-Burgers Equations Using Laplace Residual Power Series Technique |
| title_fullStr | Analytical Approximate Solutions of Caputo Fractional KdV-Burgers Equations Using Laplace Residual Power Series Technique |
| title_full_unstemmed | Analytical Approximate Solutions of Caputo Fractional KdV-Burgers Equations Using Laplace Residual Power Series Technique |
| title_short | Analytical Approximate Solutions of Caputo Fractional KdV-Burgers Equations Using Laplace Residual Power Series Technique |
| title_sort | analytical approximate solutions of caputo fractional kdv burgers equations using laplace residual power series technique |
| url | http://dx.doi.org/10.1155/2024/7835548 |
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