Analysis of Fractional-Order Regularized Long-Wave Models via a Novel Transform
A new integral transform method for regularized long-wave (RLW) models having fractional-order is presented in this study. Although analytical approaches are challenging to apply to such models, semianalytical or numerical techniques have received much attention in the literature. We propose a new t...
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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 Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2022/2754507 |
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| author | Nehad Ali Shah Essam R. El-Zahar Ali Akgül Adnan Khan Jeevan Kafle |
| author_facet | Nehad Ali Shah Essam R. El-Zahar Ali Akgül Adnan Khan Jeevan Kafle |
| author_sort | Nehad Ali Shah |
| collection | DOAJ |
| description | A new integral transform method for regularized long-wave (RLW) models having fractional-order is presented in this study. Although analytical approaches are challenging to apply to such models, semianalytical or numerical techniques have received much attention in the literature. We propose a new technique combining integral transformation, the Elzaki transform (ET), and apply it to regularized long-wave equations in this study. The RLW equations describe ion-acoustic waves in plasma and shallow water waves in seas. The results obtained are extremely important and necessary for describing various physical phenomena. This work considers an up-to-date approach and fractional operators in this context to obtain satisfactory approximate solutions to the proposed problems. We first define the Elzaki transforms of the Caputo fractional derivative (CFD) and Atangana-Baleanu fractional derivative (ABFD) and implement them for solving RLW equations. We can readily obtain numerical results that provide us with improved approximations after only a few iterations. The derived solutions were found to be in close contact with the exact solutions. Furthermore, the suggested procedure has attained the best level of accuracy. In fact, when compared to other analytical techniques for solving nonlinear fractional partial differential equations, the present method might be considered one of the finest. |
| format | Article |
| id | doaj-art-c8f6775ed1e24a34927680e23eb62aa0 |
| institution | Kabale University |
| issn | 2314-8888 |
| language | English |
| publishDate | 2022-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces |
| spelling | doaj-art-c8f6775ed1e24a34927680e23eb62aa02025-02-03T01:23:35ZengWileyJournal of Function Spaces2314-88882022-01-01202210.1155/2022/2754507Analysis of Fractional-Order Regularized Long-Wave Models via a Novel TransformNehad Ali Shah0Essam R. El-Zahar1Ali Akgül2Adnan Khan3Jeevan Kafle4Department of Mechanical EngineeringDepartment of MathematicsDepartment of MathematicsDepartment of MathematicsCentral Department of MathematicsA new integral transform method for regularized long-wave (RLW) models having fractional-order is presented in this study. Although analytical approaches are challenging to apply to such models, semianalytical or numerical techniques have received much attention in the literature. We propose a new technique combining integral transformation, the Elzaki transform (ET), and apply it to regularized long-wave equations in this study. The RLW equations describe ion-acoustic waves in plasma and shallow water waves in seas. The results obtained are extremely important and necessary for describing various physical phenomena. This work considers an up-to-date approach and fractional operators in this context to obtain satisfactory approximate solutions to the proposed problems. We first define the Elzaki transforms of the Caputo fractional derivative (CFD) and Atangana-Baleanu fractional derivative (ABFD) and implement them for solving RLW equations. We can readily obtain numerical results that provide us with improved approximations after only a few iterations. The derived solutions were found to be in close contact with the exact solutions. Furthermore, the suggested procedure has attained the best level of accuracy. In fact, when compared to other analytical techniques for solving nonlinear fractional partial differential equations, the present method might be considered one of the finest.http://dx.doi.org/10.1155/2022/2754507 |
| spellingShingle | Nehad Ali Shah Essam R. El-Zahar Ali Akgül Adnan Khan Jeevan Kafle Analysis of Fractional-Order Regularized Long-Wave Models via a Novel Transform Journal of Function Spaces |
| title | Analysis of Fractional-Order Regularized Long-Wave Models via a Novel Transform |
| title_full | Analysis of Fractional-Order Regularized Long-Wave Models via a Novel Transform |
| title_fullStr | Analysis of Fractional-Order Regularized Long-Wave Models via a Novel Transform |
| title_full_unstemmed | Analysis of Fractional-Order Regularized Long-Wave Models via a Novel Transform |
| title_short | Analysis of Fractional-Order Regularized Long-Wave Models via a Novel Transform |
| title_sort | analysis of fractional order regularized long wave models via a novel transform |
| url | http://dx.doi.org/10.1155/2022/2754507 |
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