Lucas polynomials semi-analytic solution for fractional multi-term initial value problems
Abstract Herein, we use the generalized Lucas polynomials to find an approximate numerical solution for fractional initial value problems (FIVPs). The method depends on the operational matrices for fractional differentiation and integration of generalized Lucas polynomials in the Caputo sense. We ob...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2019-11-01
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| Series: | Advances in Difference Equations |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1186/s13662-019-2402-z |
| _version_ | 1818116721271111680 |
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| author | Mahmoud M. Mokhtar Amany S. Mohamed |
| author_facet | Mahmoud M. Mokhtar Amany S. Mohamed |
| author_sort | Mahmoud M. Mokhtar |
| collection | DOAJ |
| description | Abstract Herein, we use the generalized Lucas polynomials to find an approximate numerical solution for fractional initial value problems (FIVPs). The method depends on the operational matrices for fractional differentiation and integration of generalized Lucas polynomials in the Caputo sense. We obtain these solutions using tau and collocation methods. We apply these methods by transforming the FIVP into systems of algebraic equations. The convergence and error analyses are discussed in detail. The applicability and efficiency of the method are tested and verified through numerical examples. |
| first_indexed | 2024-12-11T04:27:01Z |
| format | Article |
| id | doaj.art-a24e2d58ab9046ae8b4f5759c14dd72b |
| institution | Directory Open Access Journal |
| issn | 1687-1847 |
| language | English |
| last_indexed | 2024-12-11T04:27:01Z |
| publishDate | 2019-11-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Advances in Difference Equations |
| spelling | doaj.art-a24e2d58ab9046ae8b4f5759c14dd72b2022-12-22T01:20:58ZengSpringerOpenAdvances in Difference Equations1687-18472019-11-012019111310.1186/s13662-019-2402-zLucas polynomials semi-analytic solution for fractional multi-term initial value problemsMahmoud M. Mokhtar0Amany S. Mohamed1Department of Basic Science, Faculty of Engineering, Modern University for Technology and Information (MTI)Department of Mathematics, Faculty of Science, Helwan UniversityAbstract Herein, we use the generalized Lucas polynomials to find an approximate numerical solution for fractional initial value problems (FIVPs). The method depends on the operational matrices for fractional differentiation and integration of generalized Lucas polynomials in the Caputo sense. We obtain these solutions using tau and collocation methods. We apply these methods by transforming the FIVP into systems of algebraic equations. The convergence and error analyses are discussed in detail. The applicability and efficiency of the method are tested and verified through numerical examples.http://link.springer.com/article/10.1186/s13662-019-2402-zCaputo derivativeFractional differential equationsSpectral methodsGeneralized Lucas polynomials |
| spellingShingle | Mahmoud M. Mokhtar Amany S. Mohamed Lucas polynomials semi-analytic solution for fractional multi-term initial value problems Advances in Difference Equations Caputo derivative Fractional differential equations Spectral methods Generalized Lucas polynomials |
| title | Lucas polynomials semi-analytic solution for fractional multi-term initial value problems |
| title_full | Lucas polynomials semi-analytic solution for fractional multi-term initial value problems |
| title_fullStr | Lucas polynomials semi-analytic solution for fractional multi-term initial value problems |
| title_full_unstemmed | Lucas polynomials semi-analytic solution for fractional multi-term initial value problems |
| title_short | Lucas polynomials semi-analytic solution for fractional multi-term initial value problems |
| title_sort | lucas polynomials semi analytic solution for fractional multi term initial value problems |
| topic | Caputo derivative Fractional differential equations Spectral methods Generalized Lucas polynomials |
| url | http://link.springer.com/article/10.1186/s13662-019-2402-z |
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