Novel derivative operational matrix in Caputo sense with applications
The main objective of this study is to present a computationally efficient numerical method for solving fractional-order differential equations with initial conditions. The proposed method is based on the newly developed generalized derivative operational matrix and generalized integral operational...
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| Format: | Article |
| Language: | English |
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Taylor & Francis Group
2024-12-01
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| Series: | Journal of Taibah University for Science |
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| Online Access: | https://www.tandfonline.com/doi/10.1080/16583655.2024.2333061 |
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| author | Danish Zaidi Imran Talib Muhammad Bilal Riaz Parveen Agarwal |
| author_facet | Danish Zaidi Imran Talib Muhammad Bilal Riaz Parveen Agarwal |
| author_sort | Danish Zaidi |
| collection | DOAJ |
| description | The main objective of this study is to present a computationally efficient numerical method for solving fractional-order differential equations with initial conditions. The proposed method is based on the newly developed generalized derivative operational matrix and generalized integral operational matrix derived from Laguerre polynomials, which belong to the class of orthogonal polynomials. Through the utilization of these operational matrices, the fractional-order problems can be transformed into a system of Sylvester-type matrix equations. This system is easily solvable using any computational software, thereby providing a practical framework for solving such equations. The results obtained are compared against various benchmarks, including an existing exact solution, Podlubny numerical techniques, analytical and numerical solvers, and reported solutions from stochastic techniques employing hybrid approaches. This comparative analysis serves to validate the accuracy of our proposed design scheme. |
| format | Article |
| id | doaj-art-a838a64b724c4f1d85bb51859c74b83e |
| institution | Kabale University |
| issn | 1658-3655 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | Taylor & Francis Group |
| record_format | Article |
| series | Journal of Taibah University for Science |
| spelling | doaj-art-a838a64b724c4f1d85bb51859c74b83e2024-12-17T11:38:48ZengTaylor & Francis GroupJournal of Taibah University for Science1658-36552024-12-0118110.1080/16583655.2024.2333061Novel derivative operational matrix in Caputo sense with applicationsDanish Zaidi0Imran Talib1Muhammad Bilal Riaz2Parveen Agarwal3Department of Mathematics, University of Management and Technology, Lahore, PakistanDepartment of Mathematics, Virtual University of Pakistan, Lahore, Punjab, PakistanDepartment of Mathematics, University of Management and Technology, Lahore, PakistanDepartment of Mathematics, Anand International College of Engineering, Jaipur, IndiaThe main objective of this study is to present a computationally efficient numerical method for solving fractional-order differential equations with initial conditions. The proposed method is based on the newly developed generalized derivative operational matrix and generalized integral operational matrix derived from Laguerre polynomials, which belong to the class of orthogonal polynomials. Through the utilization of these operational matrices, the fractional-order problems can be transformed into a system of Sylvester-type matrix equations. This system is easily solvable using any computational software, thereby providing a practical framework for solving such equations. The results obtained are compared against various benchmarks, including an existing exact solution, Podlubny numerical techniques, analytical and numerical solvers, and reported solutions from stochastic techniques employing hybrid approaches. This comparative analysis serves to validate the accuracy of our proposed design scheme.https://www.tandfonline.com/doi/10.1080/16583655.2024.2333061Laguerre polynomialsoperational matricesorthogonal polynomialsspectral methodsTau methodfractional derivative differential equations |
| spellingShingle | Danish Zaidi Imran Talib Muhammad Bilal Riaz Parveen Agarwal Novel derivative operational matrix in Caputo sense with applications Journal of Taibah University for Science Laguerre polynomials operational matrices orthogonal polynomials spectral methods Tau method fractional derivative differential equations |
| title | Novel derivative operational matrix in Caputo sense with applications |
| title_full | Novel derivative operational matrix in Caputo sense with applications |
| title_fullStr | Novel derivative operational matrix in Caputo sense with applications |
| title_full_unstemmed | Novel derivative operational matrix in Caputo sense with applications |
| title_short | Novel derivative operational matrix in Caputo sense with applications |
| title_sort | novel derivative operational matrix in caputo sense with applications |
| topic | Laguerre polynomials operational matrices orthogonal polynomials spectral methods Tau method fractional derivative differential equations |
| url | https://www.tandfonline.com/doi/10.1080/16583655.2024.2333061 |
| work_keys_str_mv | AT danishzaidi novelderivativeoperationalmatrixincaputosensewithapplications AT imrantalib novelderivativeoperationalmatrixincaputosensewithapplications AT muhammadbilalriaz novelderivativeoperationalmatrixincaputosensewithapplications AT parveenagarwal novelderivativeoperationalmatrixincaputosensewithapplications |