On new aspects of Chebyshev polynomials for space-time fractional diffusion process
Chebyshev collocation scheme and Finite difference method plays central roles for solving fractional differential equations (FDE). Therefore purpose of this paper is to solve fractional mathematical problem of diffusion by Chebyshev collocation method which turns the original problems into the syste...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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Sciendo
2023-07-01
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| Series: | Applied Mathematics and Nonlinear Sciences |
| Subjects: | |
| Online Access: | https://doi.org/10.2478/amns.2021.2.00327 |
| _version_ | 1797266158970208256 |
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| author | Demir Ali Bayrak Mine Aylin Bulut Alper Ozbilge Ebru Çetinkaya Süleyman |
| author_facet | Demir Ali Bayrak Mine Aylin Bulut Alper Ozbilge Ebru Çetinkaya Süleyman |
| author_sort | Demir Ali |
| collection | DOAJ |
| description | Chebyshev collocation scheme and Finite difference method plays central roles for solving fractional differential equations (FDE). Therefore purpose of this paper is to solve fractional mathematical problem of diffusion by Chebyshev collocation method which turns the original problems into the system of fractional ordinary differential and algebraic equations by imposing orthogonality property. This system is solved by implementing Finite difference method. The numerical illustrations confirm that the combination of these two methods allow us to establish one of the best truncated solution in the series form. |
| first_indexed | 2024-03-07T16:19:53Z |
| format | Article |
| id | doaj.art-92a04c73f344435fb4913d8cccbe64e6 |
| institution | Directory Open Access Journal |
| issn | 2444-8656 |
| language | English |
| last_indexed | 2024-04-25T00:56:15Z |
| publishDate | 2023-07-01 |
| publisher | Sciendo |
| record_format | Article |
| series | Applied Mathematics and Nonlinear Sciences |
| spelling | doaj.art-92a04c73f344435fb4913d8cccbe64e62024-03-11T10:05:45ZengSciendoApplied Mathematics and Nonlinear Sciences2444-86562023-07-01821051106210.2478/amns.2021.2.00327On new aspects of Chebyshev polynomials for space-time fractional diffusion processDemir Ali0Bayrak Mine Aylin1Bulut Alper2Ozbilge Ebru3Çetinkaya Süleyman41Kocaeli University, Department of Mathematics, Izmit, Kocaeli, Turkey1Kocaeli University, Department of Mathematics, Izmit, Kocaeli, Turkey2American University of the Middle East, Department of Mathematics and Statistics, Egaila, Kuwait2American University of the Middle East, Department of Mathematics and Statistics, Egaila, Kuwait1Kocaeli University, Department of Mathematics, Izmit, Kocaeli, TurkeyChebyshev collocation scheme and Finite difference method plays central roles for solving fractional differential equations (FDE). Therefore purpose of this paper is to solve fractional mathematical problem of diffusion by Chebyshev collocation method which turns the original problems into the system of fractional ordinary differential and algebraic equations by imposing orthogonality property. This system is solved by implementing Finite difference method. The numerical illustrations confirm that the combination of these two methods allow us to establish one of the best truncated solution in the series form.https://doi.org/10.2478/amns.2021.2.00327chebyshev collocation methodspace-time fractional diffusion equationfinite differencescaputo derivatives |
| spellingShingle | Demir Ali Bayrak Mine Aylin Bulut Alper Ozbilge Ebru Çetinkaya Süleyman On new aspects of Chebyshev polynomials for space-time fractional diffusion process Applied Mathematics and Nonlinear Sciences chebyshev collocation method space-time fractional diffusion equation finite differences caputo derivatives |
| title | On new aspects of Chebyshev polynomials for space-time fractional diffusion process |
| title_full | On new aspects of Chebyshev polynomials for space-time fractional diffusion process |
| title_fullStr | On new aspects of Chebyshev polynomials for space-time fractional diffusion process |
| title_full_unstemmed | On new aspects of Chebyshev polynomials for space-time fractional diffusion process |
| title_short | On new aspects of Chebyshev polynomials for space-time fractional diffusion process |
| title_sort | on new aspects of chebyshev polynomials for space time fractional diffusion process |
| topic | chebyshev collocation method space-time fractional diffusion equation finite differences caputo derivatives |
| url | https://doi.org/10.2478/amns.2021.2.00327 |
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