Piecewise second kind Chebyshev functions for a class of piecewise fractional nonlinear reaction–diffusion equations with variable coefficients
In this paper, a new type of piecewise fractional derivative (PFD) is introduced. The ordinary and distributed-order fractional derivatives in the Caputo sense are used to define this type of PFD. A new version of nonlinear reaction–diffusion equations with variable coefficients is defined using thi...
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| Format: | Article |
| Language: | English |
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Elsevier
2025-01-01
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| Series: | Alexandria Engineering Journal |
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| Online Access: | http://www.sciencedirect.com/science/article/pii/S1110016824012717 |
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| author | M.H. Heydari D. Baleanu M. Bayramu |
| author_facet | M.H. Heydari D. Baleanu M. Bayramu |
| author_sort | M.H. Heydari |
| collection | DOAJ |
| description | In this paper, a new type of piecewise fractional derivative (PFD) is introduced. The ordinary and distributed-order fractional derivatives in the Caputo sense are used to define this type of PFD. A new version of nonlinear reaction–diffusion equations with variable coefficients is defined using this type of PFD. The orthonormal piecewise second kind Chebyshev functions (CFs), as a new family of basic functions, are generated. An explicit formula is extracted for PFD of these piecewise functions. A hybrid method based on the orthonormal piecewise second kind CFs and orthonormal second kind Chebyshev polynomials is proposed to solve the aforementioned problem. The established approach transforms solving the expressed problem into solving an algebraic system of equations. To illustrate the accuracy of the developed method, some numerical examples are considered. |
| format | Article |
| id | doaj-art-651217b182db46bf846bcbf92456ab39 |
| institution | Kabale University |
| issn | 1110-0168 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Alexandria Engineering Journal |
| spelling | doaj-art-651217b182db46bf846bcbf92456ab392025-01-29T05:00:13ZengElsevierAlexandria Engineering Journal1110-01682025-01-01112319326Piecewise second kind Chebyshev functions for a class of piecewise fractional nonlinear reaction–diffusion equations with variable coefficientsM.H. Heydari0D. Baleanu1M. Bayramu2Department of Mathematics, Shiraz University of Technology, Shiraz, Iran; Corresponding author.Department of Computer Science and Mathematics, Lebanese American University, Beirut, 13-5053, LebanonDepartment of Computer Engineering, Biruni University, Istanbul, TurkeyIn this paper, a new type of piecewise fractional derivative (PFD) is introduced. The ordinary and distributed-order fractional derivatives in the Caputo sense are used to define this type of PFD. A new version of nonlinear reaction–diffusion equations with variable coefficients is defined using this type of PFD. The orthonormal piecewise second kind Chebyshev functions (CFs), as a new family of basic functions, are generated. An explicit formula is extracted for PFD of these piecewise functions. A hybrid method based on the orthonormal piecewise second kind CFs and orthonormal second kind Chebyshev polynomials is proposed to solve the aforementioned problem. The established approach transforms solving the expressed problem into solving an algebraic system of equations. To illustrate the accuracy of the developed method, some numerical examples are considered.http://www.sciencedirect.com/science/article/pii/S1110016824012717Piecewise fractional derivativeDistributed-order fractional derivativeOrthonormal piecewise second kind Chebyshev functions |
| spellingShingle | M.H. Heydari D. Baleanu M. Bayramu Piecewise second kind Chebyshev functions for a class of piecewise fractional nonlinear reaction–diffusion equations with variable coefficients Alexandria Engineering Journal Piecewise fractional derivative Distributed-order fractional derivative Orthonormal piecewise second kind Chebyshev functions |
| title | Piecewise second kind Chebyshev functions for a class of piecewise fractional nonlinear reaction–diffusion equations with variable coefficients |
| title_full | Piecewise second kind Chebyshev functions for a class of piecewise fractional nonlinear reaction–diffusion equations with variable coefficients |
| title_fullStr | Piecewise second kind Chebyshev functions for a class of piecewise fractional nonlinear reaction–diffusion equations with variable coefficients |
| title_full_unstemmed | Piecewise second kind Chebyshev functions for a class of piecewise fractional nonlinear reaction–diffusion equations with variable coefficients |
| title_short | Piecewise second kind Chebyshev functions for a class of piecewise fractional nonlinear reaction–diffusion equations with variable coefficients |
| title_sort | piecewise second kind chebyshev functions for a class of piecewise fractional nonlinear reaction diffusion equations with variable coefficients |
| topic | Piecewise fractional derivative Distributed-order fractional derivative Orthonormal piecewise second kind Chebyshev functions |
| url | http://www.sciencedirect.com/science/article/pii/S1110016824012717 |
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