Analysis of Fractional Kundu-Eckhaus and Massive Thirring Equations Using a Hybridization Scheme
This paper deals with the study of fractional Kundu-Eckhaus equation (FKEE) and fractional massive Thirring problem (FMTP) that appear in the quantum field theory, weakly nonlinear dispersive water waves, and nonlinear optics. Since the variational iteration method involves integration, the Laplace...
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| Format: | Article |
| Language: | English |
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Wiley
2023-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2023/6704537 |
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| _version_ | 1832548003325411328 |
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| author | Muhammad Nadeem Hanan A. Wahash |
| author_facet | Muhammad Nadeem Hanan A. Wahash |
| author_sort | Muhammad Nadeem |
| collection | DOAJ |
| description | This paper deals with the study of fractional Kundu-Eckhaus equation (FKEE) and fractional massive Thirring problem (FMTP) that appear in the quantum field theory, weakly nonlinear dispersive water waves, and nonlinear optics. Since the variational iteration method involves integration, the Laplace transform involves convolution theorem in recurrence relation to derive the series solution. To avoid some assumptions and hypothesis, we apply a two-scale approach for such a nonlinear complex model. The fractional differential equation may be transformed into its partner equation using He’s fractional complex transform, and then, the nonlinear elements can be readily handled using the homotopy perturbation method (HPM). Numerical results are derived in a rapid converge series form to improve the accuracy of the scheme greatly. Graphical representations and error distribution show that the two-scale approach is a very convenient tool. |
| format | Article |
| id | doaj-art-9fd336484b6c4c38803a72d27131e847 |
| institution | Kabale University |
| issn | 2314-8888 |
| language | English |
| publishDate | 2023-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces |
| spelling | doaj-art-9fd336484b6c4c38803a72d27131e8472025-02-03T06:42:39ZengWileyJournal of Function Spaces2314-88882023-01-01202310.1155/2023/6704537Analysis of Fractional Kundu-Eckhaus and Massive Thirring Equations Using a Hybridization SchemeMuhammad Nadeem0Hanan A. Wahash1School of Mathematics and StatisticsDepartment of MathematicsThis paper deals with the study of fractional Kundu-Eckhaus equation (FKEE) and fractional massive Thirring problem (FMTP) that appear in the quantum field theory, weakly nonlinear dispersive water waves, and nonlinear optics. Since the variational iteration method involves integration, the Laplace transform involves convolution theorem in recurrence relation to derive the series solution. To avoid some assumptions and hypothesis, we apply a two-scale approach for such a nonlinear complex model. The fractional differential equation may be transformed into its partner equation using He’s fractional complex transform, and then, the nonlinear elements can be readily handled using the homotopy perturbation method (HPM). Numerical results are derived in a rapid converge series form to improve the accuracy of the scheme greatly. Graphical representations and error distribution show that the two-scale approach is a very convenient tool.http://dx.doi.org/10.1155/2023/6704537 |
| spellingShingle | Muhammad Nadeem Hanan A. Wahash Analysis of Fractional Kundu-Eckhaus and Massive Thirring Equations Using a Hybridization Scheme Journal of Function Spaces |
| title | Analysis of Fractional Kundu-Eckhaus and Massive Thirring Equations Using a Hybridization Scheme |
| title_full | Analysis of Fractional Kundu-Eckhaus and Massive Thirring Equations Using a Hybridization Scheme |
| title_fullStr | Analysis of Fractional Kundu-Eckhaus and Massive Thirring Equations Using a Hybridization Scheme |
| title_full_unstemmed | Analysis of Fractional Kundu-Eckhaus and Massive Thirring Equations Using a Hybridization Scheme |
| title_short | Analysis of Fractional Kundu-Eckhaus and Massive Thirring Equations Using a Hybridization Scheme |
| title_sort | analysis of fractional kundu eckhaus and massive thirring equations using a hybridization scheme |
| url | http://dx.doi.org/10.1155/2023/6704537 |
| work_keys_str_mv | AT muhammadnadeem analysisoffractionalkundueckhausandmassivethirringequationsusingahybridizationscheme AT hananawahash analysisoffractionalkundueckhausandmassivethirringequationsusingahybridizationscheme |