Fractional Dynamical Systems Solved by a Collocation Method Based on Refinable Spaces
A dynamical system is a particle or set of particles whose state changes over time. The dynamics of the system is described by a set of differential equations. If the derivatives involved are of non-integer order, we obtain a fractional dynamical system. In this paper, we considered a fractional dyn...
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MDPI AG
2023-05-01
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| Online Access: | https://www.mdpi.com/2075-1680/12/5/451 |
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| author | Laura Pezza Simmaco Di Lillo |
| author_facet | Laura Pezza Simmaco Di Lillo |
| author_sort | Laura Pezza |
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| description | A dynamical system is a particle or set of particles whose state changes over time. The dynamics of the system is described by a set of differential equations. If the derivatives involved are of non-integer order, we obtain a fractional dynamical system. In this paper, we considered a fractional dynamical system with the Caputo fractional derivative. We collocated the fractional differential problem in dyadic nodes and used refinable functions as approximation functions to achieve a good degree of freedom in the choice of the regularity. The collocation method stands out as a particularly useful and attractive tool for solving fractional differential problems of various forms. A numerical result is presented to show that the numerical solution fits the analytical one very well. We collocated the fractional differential problem in dyadic nodes using refinable functions as approximation functions to achieve a good degree of freedom in the choice of regularity. |
| first_indexed | 2024-03-11T03:56:30Z |
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| institution | Directory Open Access Journal |
| issn | 2075-1680 |
| language | English |
| last_indexed | 2024-03-11T03:56:30Z |
| publishDate | 2023-05-01 |
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| spelling | doaj.art-3721589cc7cd4729a22a7ecc1b73fb2e2023-11-18T00:27:28ZengMDPI AGAxioms2075-16802023-05-0112545110.3390/axioms12050451Fractional Dynamical Systems Solved by a Collocation Method Based on Refinable SpacesLaura Pezza0Simmaco Di Lillo1Department of Basic and Applied Sciences for Engineering (SBAI), Università di Roma “La Sapienza”, Via A. Scarpa 16, 00161 Rome, ItalyDepartment of Mathematics Guido Castelnuovo, Università di Roma “La Sapienza”, Piazzale Aldo Moro 5, 00185 Rome, ItalyA dynamical system is a particle or set of particles whose state changes over time. The dynamics of the system is described by a set of differential equations. If the derivatives involved are of non-integer order, we obtain a fractional dynamical system. In this paper, we considered a fractional dynamical system with the Caputo fractional derivative. We collocated the fractional differential problem in dyadic nodes and used refinable functions as approximation functions to achieve a good degree of freedom in the choice of the regularity. The collocation method stands out as a particularly useful and attractive tool for solving fractional differential problems of various forms. A numerical result is presented to show that the numerical solution fits the analytical one very well. We collocated the fractional differential problem in dyadic nodes using refinable functions as approximation functions to achieve a good degree of freedom in the choice of regularity.https://www.mdpi.com/2075-1680/12/5/451fractional differential problemcollocation methodfractional derivativeB-spline |
| spellingShingle | Laura Pezza Simmaco Di Lillo Fractional Dynamical Systems Solved by a Collocation Method Based on Refinable Spaces Axioms fractional differential problem collocation method fractional derivative B-spline |
| title | Fractional Dynamical Systems Solved by a Collocation Method Based on Refinable Spaces |
| title_full | Fractional Dynamical Systems Solved by a Collocation Method Based on Refinable Spaces |
| title_fullStr | Fractional Dynamical Systems Solved by a Collocation Method Based on Refinable Spaces |
| title_full_unstemmed | Fractional Dynamical Systems Solved by a Collocation Method Based on Refinable Spaces |
| title_short | Fractional Dynamical Systems Solved by a Collocation Method Based on Refinable Spaces |
| title_sort | fractional dynamical systems solved by a collocation method based on refinable spaces |
| topic | fractional differential problem collocation method fractional derivative B-spline |
| url | https://www.mdpi.com/2075-1680/12/5/451 |
| work_keys_str_mv | AT laurapezza fractionaldynamicalsystemssolvedbyacollocationmethodbasedonrefinablespaces AT simmacodilillo fractionaldynamicalsystemssolvedbyacollocationmethodbasedonrefinablespaces |