Pell Collocation Method for Solving the Nonlinear Time–Fractional Partial Integro–Differential Equation with a Weakly Singular Kernel
This article focuses on finding the numerical solution of the nonlinear time–fractional partial integro–differential equation. For this purpose, we use the operational matrices based on Pell polynomials to approximate fractional Caputo derivative, nonlinear, and integro–differential terms; and by co...
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| Main Authors: | , |
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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/10.1155/2022/8063888 |
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| _version_ | 1832553638811140096 |
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| author | M. Taghipour H. Aminikhah |
| author_facet | M. Taghipour H. Aminikhah |
| author_sort | M. Taghipour |
| collection | DOAJ |
| description | This article focuses on finding the numerical solution of the nonlinear time–fractional partial integro–differential equation. For this purpose, we use the operational matrices based on Pell polynomials to approximate fractional Caputo derivative, nonlinear, and integro–differential terms; and by collocation points, we transform the problem to a system of nonlinear equations. This nonlinear system can be solved by the fsolve command in Matlab. The method’s stability and convergence have been studied. Also included are five numerical examples to demonstrate the veracity of the suggested strategy. |
| format | Article |
| id | doaj-art-d05080d67a664716a81f6d01cce65d06 |
| 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-d05080d67a664716a81f6d01cce65d062025-02-03T05:53:38ZengWileyJournal of Function Spaces2314-88882022-01-01202210.1155/2022/8063888Pell Collocation Method for Solving the Nonlinear Time–Fractional Partial Integro–Differential Equation with a Weakly Singular KernelM. Taghipour0H. Aminikhah1Department of Applied Mathematics and Computer ScienceDepartment of Applied Mathematics and Computer ScienceThis article focuses on finding the numerical solution of the nonlinear time–fractional partial integro–differential equation. For this purpose, we use the operational matrices based on Pell polynomials to approximate fractional Caputo derivative, nonlinear, and integro–differential terms; and by collocation points, we transform the problem to a system of nonlinear equations. This nonlinear system can be solved by the fsolve command in Matlab. The method’s stability and convergence have been studied. Also included are five numerical examples to demonstrate the veracity of the suggested strategy.http://dx.doi.org/10.1155/2022/8063888 |
| spellingShingle | M. Taghipour H. Aminikhah Pell Collocation Method for Solving the Nonlinear Time–Fractional Partial Integro–Differential Equation with a Weakly Singular Kernel Journal of Function Spaces |
| title | Pell Collocation Method for Solving the Nonlinear Time–Fractional Partial Integro–Differential Equation with a Weakly Singular Kernel |
| title_full | Pell Collocation Method for Solving the Nonlinear Time–Fractional Partial Integro–Differential Equation with a Weakly Singular Kernel |
| title_fullStr | Pell Collocation Method for Solving the Nonlinear Time–Fractional Partial Integro–Differential Equation with a Weakly Singular Kernel |
| title_full_unstemmed | Pell Collocation Method for Solving the Nonlinear Time–Fractional Partial Integro–Differential Equation with a Weakly Singular Kernel |
| title_short | Pell Collocation Method for Solving the Nonlinear Time–Fractional Partial Integro–Differential Equation with a Weakly Singular Kernel |
| title_sort | pell collocation method for solving the nonlinear time fractional partial integro differential equation with a weakly singular kernel |
| url | http://dx.doi.org/10.1155/2022/8063888 |
| work_keys_str_mv | AT mtaghipour pellcollocationmethodforsolvingthenonlineartimefractionalpartialintegrodifferentialequationwithaweaklysingularkernel AT haminikhah pellcollocationmethodforsolvingthenonlineartimefractionalpartialintegrodifferentialequationwithaweaklysingularkernel |