Kronecker operational matrices for fractional calculus and some applications
The problems of systems identification, analysis and optimal control have been recently studied using orthogonal functions. The specific orthogonal functions used up to now are the Walsh, the block-pulse, the Laguerre, the Legendre, Haar and many other functions. In the present paper, several operat...
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| Format: | Article |
| Language: | English |
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Elsevier
2007
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| Online Access: | http://psasir.upm.edu.my/id/eprint/8692/1/Kronecker%20operational%20matrices%20for%20fractional%20calculus%20and%20some%20applications.pdf |
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| author | Kilicman, Adem Abdel Aziz Al Zhour, Zeyad |
| author_facet | Kilicman, Adem Abdel Aziz Al Zhour, Zeyad |
| author_sort | Kilicman, Adem |
| collection | UPM |
| description | The problems of systems identification, analysis and optimal control have been recently studied using orthogonal functions. The specific orthogonal functions used up to now are the Walsh, the block-pulse, the Laguerre, the Legendre, Haar and many other functions. In the present paper, several operational matrices for integration and differentiation are studied. we introduce the Kronecker convolution product and expanded to the Riemann-Liouville fractional integral of matrices. For some applications, it is often not necessary to compute exact solutions, approximate solutions are sufficient because sometimes computational efforts rapidly increase with the size of matrix functions. Our method is extended to find the exact and approximate solutions of the general system matrix convolution differential equations, the way exists which transform the coupled matrix differential equations into forms for which solutions may be readily computed. Finally, several systems are solved by the new and other approaches and illustrative examples are also considered. |
| first_indexed | 2024-03-06T07:15:58Z |
| format | Article |
| id | upm.eprints-8692 |
| institution | Universiti Putra Malaysia |
| language | English |
| last_indexed | 2024-03-06T07:15:58Z |
| publishDate | 2007 |
| publisher | Elsevier |
| record_format | dspace |
| spelling | upm.eprints-86922016-02-03T01:50:58Z http://psasir.upm.edu.my/id/eprint/8692/ Kronecker operational matrices for fractional calculus and some applications Kilicman, Adem Abdel Aziz Al Zhour, Zeyad The problems of systems identification, analysis and optimal control have been recently studied using orthogonal functions. The specific orthogonal functions used up to now are the Walsh, the block-pulse, the Laguerre, the Legendre, Haar and many other functions. In the present paper, several operational matrices for integration and differentiation are studied. we introduce the Kronecker convolution product and expanded to the Riemann-Liouville fractional integral of matrices. For some applications, it is often not necessary to compute exact solutions, approximate solutions are sufficient because sometimes computational efforts rapidly increase with the size of matrix functions. Our method is extended to find the exact and approximate solutions of the general system matrix convolution differential equations, the way exists which transform the coupled matrix differential equations into forms for which solutions may be readily computed. Finally, several systems are solved by the new and other approaches and illustrative examples are also considered. Elsevier 2007-04-01 Article PeerReviewed application/pdf en http://psasir.upm.edu.my/id/eprint/8692/1/Kronecker%20operational%20matrices%20for%20fractional%20calculus%20and%20some%20applications.pdf Kilicman, Adem and Abdel Aziz Al Zhour, Zeyad (2007) Kronecker operational matrices for fractional calculus and some applications. Applied Mathematics and Computation, 187 (1). pp. 250-265. ISSN 0096-3003 http://dx.doi.org/10.1016/j.amc.2006.08.122 10.1016/j.amc.2006.08.122 |
| spellingShingle | Kilicman, Adem Abdel Aziz Al Zhour, Zeyad Kronecker operational matrices for fractional calculus and some applications |
| title | Kronecker operational matrices for fractional calculus and some applications |
| title_full | Kronecker operational matrices for fractional calculus and some applications |
| title_fullStr | Kronecker operational matrices for fractional calculus and some applications |
| title_full_unstemmed | Kronecker operational matrices for fractional calculus and some applications |
| title_short | Kronecker operational matrices for fractional calculus and some applications |
| title_sort | kronecker operational matrices for fractional calculus and some applications |
| url | http://psasir.upm.edu.my/id/eprint/8692/1/Kronecker%20operational%20matrices%20for%20fractional%20calculus%20and%20some%20applications.pdf |
| work_keys_str_mv | AT kilicmanadem kroneckeroperationalmatricesforfractionalcalculusandsomeapplications AT abdelazizalzhourzeyad kroneckeroperationalmatricesforfractionalcalculusandsomeapplications |