An Effective Method for Solving Fractional Integrodifferential Equations of the Volterra and Fredholm Types Based on the Lucas Polynomials
This article extends a spectral collocation approach based on Lucas polynomials to numerically solve the integrodifferential equations of both Volterra and Fredholm types for multi–higher fractional order in the Caputo sense under the mixed conditions. The new approach focusses on using a matrix str...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2025-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/jama/6805724 |
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| author | Shabaz Jalil Mohammedfaeq Miran Bayan Mohammed Amin Dashne Chapuk Zahir Shazad Shawki Ahmed |
| author_facet | Shabaz Jalil Mohammedfaeq Miran Bayan Mohammed Amin Dashne Chapuk Zahir Shazad Shawki Ahmed |
| author_sort | Shabaz Jalil Mohammedfaeq |
| collection | DOAJ |
| description | This article extends a spectral collocation approach based on Lucas polynomials to numerically solve the integrodifferential equations of both Volterra and Fredholm types for multi–higher fractional order in the Caputo sense under the mixed conditions. The new approach focusses on using a matrix strategy to convert the supplied equation with conditions into an algebraic linear system of equations with unknown Lucas coefficients. The coefficients of the presumed solution are determined by the solution of this system. The Lucas coefficients are used to track how the solutions behave. This method is attractive for computation, and usage examples and explanations are provided. Additionally, certain examples are provided to demonstrate the method’s accuracy, and the least-squares error technique is employed to reduce error terms inside the designated domain. Because of this, Python is used to write most general programs. |
| format | Article |
| id | doaj-art-17fd16b07d2b4aaeac3ada5b6e7d1fa1 |
| institution | OA Journals |
| issn | 1687-0042 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-17fd16b07d2b4aaeac3ada5b6e7d1fa12025-08-20T02:10:30ZengWileyJournal of Applied Mathematics1687-00422025-01-01202510.1155/jama/6805724An Effective Method for Solving Fractional Integrodifferential Equations of the Volterra and Fredholm Types Based on the Lucas PolynomialsShabaz Jalil Mohammedfaeq0Miran Bayan Mohammed Amin1Dashne Chapuk Zahir2Shazad Shawki Ahmed3Department of MathematicsTechnical College of InformaticsDepartment of MathematicsDepartment of MathematicsThis article extends a spectral collocation approach based on Lucas polynomials to numerically solve the integrodifferential equations of both Volterra and Fredholm types for multi–higher fractional order in the Caputo sense under the mixed conditions. The new approach focusses on using a matrix strategy to convert the supplied equation with conditions into an algebraic linear system of equations with unknown Lucas coefficients. The coefficients of the presumed solution are determined by the solution of this system. The Lucas coefficients are used to track how the solutions behave. This method is attractive for computation, and usage examples and explanations are provided. Additionally, certain examples are provided to demonstrate the method’s accuracy, and the least-squares error technique is employed to reduce error terms inside the designated domain. Because of this, Python is used to write most general programs.http://dx.doi.org/10.1155/jama/6805724 |
| spellingShingle | Shabaz Jalil Mohammedfaeq Miran Bayan Mohammed Amin Dashne Chapuk Zahir Shazad Shawki Ahmed An Effective Method for Solving Fractional Integrodifferential Equations of the Volterra and Fredholm Types Based on the Lucas Polynomials Journal of Applied Mathematics |
| title | An Effective Method for Solving Fractional Integrodifferential Equations of the Volterra and Fredholm Types Based on the Lucas Polynomials |
| title_full | An Effective Method for Solving Fractional Integrodifferential Equations of the Volterra and Fredholm Types Based on the Lucas Polynomials |
| title_fullStr | An Effective Method for Solving Fractional Integrodifferential Equations of the Volterra and Fredholm Types Based on the Lucas Polynomials |
| title_full_unstemmed | An Effective Method for Solving Fractional Integrodifferential Equations of the Volterra and Fredholm Types Based on the Lucas Polynomials |
| title_short | An Effective Method for Solving Fractional Integrodifferential Equations of the Volterra and Fredholm Types Based on the Lucas Polynomials |
| title_sort | effective method for solving fractional integrodifferential equations of the volterra and fredholm types based on the lucas polynomials |
| url | http://dx.doi.org/10.1155/jama/6805724 |
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