Chebyshev Polynomials of Sixth Kind for Solving Nonlinear Fractional PDEs with Proportional Delay and Its Convergence Analysis
This work devotes to solving a class of delay fractional partial differential equations that arises in physical, biological, medical, and climate models. For this, a numerical scheme is implemented that applies operational matrices to convert the main problem into a system of algebraic equations; th...
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| Format: | Article |
| Language: | English |
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Wiley
2022-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2022/9512048 |
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| _version_ | 1849387164879552512 |
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| author | Khadijeh Sadri Hossein Aminikhah |
| author_facet | Khadijeh Sadri Hossein Aminikhah |
| author_sort | Khadijeh Sadri |
| collection | DOAJ |
| description | This work devotes to solving a class of delay fractional partial differential equations that arises in physical, biological, medical, and climate models. For this, a numerical scheme is implemented that applies operational matrices to convert the main problem into a system of algebraic equations; then, solving the resultant system leads to an approximate solution. The two-variable Chebyshev polynomials of the sixth kind, as basis functions in the proposed method, are constructed by the one-variable ones, and their operational matrices are derived. Error bounds of approximate solutions and their fractional and classical derivatives are computed. With the aid of these bounds, a bound for the residual function is estimated. Three illustrative examples demonstrate the simplicity and efficiency of the proposed method. |
| format | Article |
| id | doaj-art-3317c2c0d938445bb1a2c101272143e8 |
| institution | Kabale University |
| issn | 2314-8888 |
| language | English |
| publishDate | 2022-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces |
| spelling | doaj-art-3317c2c0d938445bb1a2c101272143e82025-08-20T03:55:17ZengWileyJournal of Function Spaces2314-88882022-01-01202210.1155/2022/9512048Chebyshev Polynomials of Sixth Kind for Solving Nonlinear Fractional PDEs with Proportional Delay and Its Convergence AnalysisKhadijeh Sadri0Hossein Aminikhah1Department of Applied Mathematics and Computer ScienceDepartment of Applied Mathematics and Computer ScienceThis work devotes to solving a class of delay fractional partial differential equations that arises in physical, biological, medical, and climate models. For this, a numerical scheme is implemented that applies operational matrices to convert the main problem into a system of algebraic equations; then, solving the resultant system leads to an approximate solution. The two-variable Chebyshev polynomials of the sixth kind, as basis functions in the proposed method, are constructed by the one-variable ones, and their operational matrices are derived. Error bounds of approximate solutions and their fractional and classical derivatives are computed. With the aid of these bounds, a bound for the residual function is estimated. Three illustrative examples demonstrate the simplicity and efficiency of the proposed method.http://dx.doi.org/10.1155/2022/9512048 |
| spellingShingle | Khadijeh Sadri Hossein Aminikhah Chebyshev Polynomials of Sixth Kind for Solving Nonlinear Fractional PDEs with Proportional Delay and Its Convergence Analysis Journal of Function Spaces |
| title | Chebyshev Polynomials of Sixth Kind for Solving Nonlinear Fractional PDEs with Proportional Delay and Its Convergence Analysis |
| title_full | Chebyshev Polynomials of Sixth Kind for Solving Nonlinear Fractional PDEs with Proportional Delay and Its Convergence Analysis |
| title_fullStr | Chebyshev Polynomials of Sixth Kind for Solving Nonlinear Fractional PDEs with Proportional Delay and Its Convergence Analysis |
| title_full_unstemmed | Chebyshev Polynomials of Sixth Kind for Solving Nonlinear Fractional PDEs with Proportional Delay and Its Convergence Analysis |
| title_short | Chebyshev Polynomials of Sixth Kind for Solving Nonlinear Fractional PDEs with Proportional Delay and Its Convergence Analysis |
| title_sort | chebyshev polynomials of sixth kind for solving nonlinear fractional pdes with proportional delay and its convergence analysis |
| url | http://dx.doi.org/10.1155/2022/9512048 |
| work_keys_str_mv | AT khadijehsadri chebyshevpolynomialsofsixthkindforsolvingnonlinearfractionalpdeswithproportionaldelayanditsconvergenceanalysis AT hosseinaminikhah chebyshevpolynomialsofsixthkindforsolvingnonlinearfractionalpdeswithproportionaldelayanditsconvergenceanalysis |