Semianalytical Solutions of Some Nonlinear-Time Fractional Models Using Variational Iteration Laplace Transform Method
In this work, we combined two techniques, the variational iteration technique and the Laplace transform method, in order to solve some nonlinear-time fractional partial differential equations. Although the exact solutions may exist, we introduced the technique VITM that approximates the solutions th...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Wiley
2021-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2021/8345682 |
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| _version_ | 1832560109500235776 |
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| author | Javed Iqbal Khurram Shabbir Liliana Guran |
| author_facet | Javed Iqbal Khurram Shabbir Liliana Guran |
| author_sort | Javed Iqbal |
| collection | DOAJ |
| description | In this work, we combined two techniques, the variational iteration technique and the Laplace transform method, in order to solve some nonlinear-time fractional partial differential equations. Although the exact solutions may exist, we introduced the technique VITM that approximates the solutions that are difficult to find. Even a single iteration best approximates the exact solutions. The fractional derivatives being used are in the Caputo-Fabrizio sense. The reliability and efficiency of this newly introduced method is discussed in details from its numerical results and their graphical approximations. Moreover, possible consequences of these results as an application of fixed-point theorem are placed before the experts as an open problem. |
| format | Article |
| id | doaj-art-5b51f01ec632437aa29e6e616929357b |
| institution | Kabale University |
| issn | 2314-8888 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces |
| spelling | doaj-art-5b51f01ec632437aa29e6e616929357b2025-02-03T01:28:22ZengWileyJournal of Function Spaces2314-88882021-01-01202110.1155/2021/8345682Semianalytical Solutions of Some Nonlinear-Time Fractional Models Using Variational Iteration Laplace Transform MethodJaved Iqbal0Khurram Shabbir1Liliana Guran2Department of MathematicsDepartment of MathematicsDepartment of Pharmaceutical SciencesIn this work, we combined two techniques, the variational iteration technique and the Laplace transform method, in order to solve some nonlinear-time fractional partial differential equations. Although the exact solutions may exist, we introduced the technique VITM that approximates the solutions that are difficult to find. Even a single iteration best approximates the exact solutions. The fractional derivatives being used are in the Caputo-Fabrizio sense. The reliability and efficiency of this newly introduced method is discussed in details from its numerical results and their graphical approximations. Moreover, possible consequences of these results as an application of fixed-point theorem are placed before the experts as an open problem.http://dx.doi.org/10.1155/2021/8345682 |
| spellingShingle | Javed Iqbal Khurram Shabbir Liliana Guran Semianalytical Solutions of Some Nonlinear-Time Fractional Models Using Variational Iteration Laplace Transform Method Journal of Function Spaces |
| title | Semianalytical Solutions of Some Nonlinear-Time Fractional Models Using Variational Iteration Laplace Transform Method |
| title_full | Semianalytical Solutions of Some Nonlinear-Time Fractional Models Using Variational Iteration Laplace Transform Method |
| title_fullStr | Semianalytical Solutions of Some Nonlinear-Time Fractional Models Using Variational Iteration Laplace Transform Method |
| title_full_unstemmed | Semianalytical Solutions of Some Nonlinear-Time Fractional Models Using Variational Iteration Laplace Transform Method |
| title_short | Semianalytical Solutions of Some Nonlinear-Time Fractional Models Using Variational Iteration Laplace Transform Method |
| title_sort | semianalytical solutions of some nonlinear time fractional models using variational iteration laplace transform method |
| url | http://dx.doi.org/10.1155/2021/8345682 |
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