Numerical solutions of fractional optimal control with Caputo–Katugampola derivative
Abstract In this paper, we present a numerical technique for solving fractional optimal control problems with a fractional derivative called Caputo–Katugampola derivative. This derivative is a generalization of the Caputo fractional derivative. The proposed technique is based on a spectral method us...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2021-09-01
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| Series: | Advances in Difference Equations |
| Subjects: | |
| Online Access: | https://doi.org/10.1186/s13662-021-03580-w |
| _version_ | 1819111049479061504 |
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| author | N. H. Sweilam A. M. Nagy T. M. Al-Ajami |
| author_facet | N. H. Sweilam A. M. Nagy T. M. Al-Ajami |
| author_sort | N. H. Sweilam |
| collection | DOAJ |
| description | Abstract In this paper, we present a numerical technique for solving fractional optimal control problems with a fractional derivative called Caputo–Katugampola derivative. This derivative is a generalization of the Caputo fractional derivative. The proposed technique is based on a spectral method using shifted Chebyshev polynomials of the first kind. The Clenshaw and Curtis scheme for the numerical integration and the Rayleigh–Ritz method are used to estimate the state and control variables. Moreover, the error bound of the fractional derivative operator approximation of Caputo–Katugampola is derived. Illustrative examples are provided to show the validity and applicability of the presented technique. |
| first_indexed | 2024-12-22T03:51:26Z |
| format | Article |
| id | doaj.art-fda76998625749e5af970dd0834e8293 |
| institution | Directory Open Access Journal |
| issn | 1687-1847 |
| language | English |
| last_indexed | 2024-12-22T03:51:26Z |
| publishDate | 2021-09-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Advances in Difference Equations |
| spelling | doaj.art-fda76998625749e5af970dd0834e82932022-12-21T18:39:59ZengSpringerOpenAdvances in Difference Equations1687-18472021-09-012021111610.1186/s13662-021-03580-wNumerical solutions of fractional optimal control with Caputo–Katugampola derivativeN. H. Sweilam0A. M. Nagy1T. M. Al-Ajami2Department of Mathematics, Faculty of Science, Cairo UniversityDepartment of Mathematics, Faculty of Science, Kuwait UniversityDepartment of Mathematics, Faculty of Science, Cairo UniversityAbstract In this paper, we present a numerical technique for solving fractional optimal control problems with a fractional derivative called Caputo–Katugampola derivative. This derivative is a generalization of the Caputo fractional derivative. The proposed technique is based on a spectral method using shifted Chebyshev polynomials of the first kind. The Clenshaw and Curtis scheme for the numerical integration and the Rayleigh–Ritz method are used to estimate the state and control variables. Moreover, the error bound of the fractional derivative operator approximation of Caputo–Katugampola is derived. Illustrative examples are provided to show the validity and applicability of the presented technique.https://doi.org/10.1186/s13662-021-03580-wCaputo–Katugampola fractional derivativeFractional optimal control problemsChebyshev expansionSpectral methods |
| spellingShingle | N. H. Sweilam A. M. Nagy T. M. Al-Ajami Numerical solutions of fractional optimal control with Caputo–Katugampola derivative Advances in Difference Equations Caputo–Katugampola fractional derivative Fractional optimal control problems Chebyshev expansion Spectral methods |
| title | Numerical solutions of fractional optimal control with Caputo–Katugampola derivative |
| title_full | Numerical solutions of fractional optimal control with Caputo–Katugampola derivative |
| title_fullStr | Numerical solutions of fractional optimal control with Caputo–Katugampola derivative |
| title_full_unstemmed | Numerical solutions of fractional optimal control with Caputo–Katugampola derivative |
| title_short | Numerical solutions of fractional optimal control with Caputo–Katugampola derivative |
| title_sort | numerical solutions of fractional optimal control with caputo katugampola derivative |
| topic | Caputo–Katugampola fractional derivative Fractional optimal control problems Chebyshev expansion Spectral methods |
| url | https://doi.org/10.1186/s13662-021-03580-w |
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