Orthonormal Chelyshkov polynomials for multi-term time fractional two-dimensional telegraph type equations
In this study, multi-term time fractional 2D telegraph type equations, as a new category of fractional differential equations, are introduced. The orthonormal Chelyshkov polynomials are used as basis functions to generate a collocation method for such equations. In this way, new results are obtained...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Elsevier
2023-12-01
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| Series: | Results in Physics |
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| Online Access: | http://www.sciencedirect.com/science/article/pii/S2211379723009543 |
| _version_ | 1797430042821656576 |
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| author | M.H. Heydari M. Razzaghi Sh. Karami |
| author_facet | M.H. Heydari M. Razzaghi Sh. Karami |
| author_sort | M.H. Heydari |
| collection | DOAJ |
| description | In this study, multi-term time fractional 2D telegraph type equations, as a new category of fractional differential equations, are introduced. The orthonormal Chelyshkov polynomials are used as basis functions to generate a collocation method for such equations. In this way, new results are obtained for the fractional and classical derivatives of these polynomials. In the proposed method, by representing the problem’s solution in terms of the orthonormal Chelyshkov polynomials (with unknown coefficients) and applying the extracted matrices, along with the collocation method, a solution is elicited for the problem under consideration. In fact, finding the solution of the initial problem turns into assigning the expansion coefficients through solving a system of algebraic equations. The accuracy of the proposed method is numerically checked with several examples. |
| first_indexed | 2024-03-09T09:21:57Z |
| format | Article |
| id | doaj.art-3823a59cefad4ec0b082b70923a769eb |
| institution | Directory Open Access Journal |
| issn | 2211-3797 |
| language | English |
| last_indexed | 2024-03-09T09:21:57Z |
| publishDate | 2023-12-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Results in Physics |
| spelling | doaj.art-3823a59cefad4ec0b082b70923a769eb2023-12-02T06:59:34ZengElsevierResults in Physics2211-37972023-12-0155107161Orthonormal Chelyshkov polynomials for multi-term time fractional two-dimensional telegraph type equationsM.H. Heydari0M. Razzaghi1Sh. Karami2Department of Mathematics, Shiraz University of Technology, Shiraz, Iran; Corresponding author.Department of Mathematics and Statistics, Mississippi State University, Mississippi State, MS 39762, USADepartment of Mathematics, Shiraz University of Technology, Shiraz, IranIn this study, multi-term time fractional 2D telegraph type equations, as a new category of fractional differential equations, are introduced. The orthonormal Chelyshkov polynomials are used as basis functions to generate a collocation method for such equations. In this way, new results are obtained for the fractional and classical derivatives of these polynomials. In the proposed method, by representing the problem’s solution in terms of the orthonormal Chelyshkov polynomials (with unknown coefficients) and applying the extracted matrices, along with the collocation method, a solution is elicited for the problem under consideration. In fact, finding the solution of the initial problem turns into assigning the expansion coefficients through solving a system of algebraic equations. The accuracy of the proposed method is numerically checked with several examples.http://www.sciencedirect.com/science/article/pii/S2211379723009543Chelyshkov polynomialsMulti-term time fractional telegraph type equationsOperational matrices |
| spellingShingle | M.H. Heydari M. Razzaghi Sh. Karami Orthonormal Chelyshkov polynomials for multi-term time fractional two-dimensional telegraph type equations Results in Physics Chelyshkov polynomials Multi-term time fractional telegraph type equations Operational matrices |
| title | Orthonormal Chelyshkov polynomials for multi-term time fractional two-dimensional telegraph type equations |
| title_full | Orthonormal Chelyshkov polynomials for multi-term time fractional two-dimensional telegraph type equations |
| title_fullStr | Orthonormal Chelyshkov polynomials for multi-term time fractional two-dimensional telegraph type equations |
| title_full_unstemmed | Orthonormal Chelyshkov polynomials for multi-term time fractional two-dimensional telegraph type equations |
| title_short | Orthonormal Chelyshkov polynomials for multi-term time fractional two-dimensional telegraph type equations |
| title_sort | orthonormal chelyshkov polynomials for multi term time fractional two dimensional telegraph type equations |
| topic | Chelyshkov polynomials Multi-term time fractional telegraph type equations Operational matrices |
| url | http://www.sciencedirect.com/science/article/pii/S2211379723009543 |
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