Fractional vs. Ordinary Control Systems: What Does the Fractional Derivative Provide?
The concept of a fractional derivative is not at all intuitive, starting with not having a clear geometrical interpretation. Many different definitions have appeared, to the point that the need for order has arisen in the field. The diversity of potential applications is even more overwhelming. When...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-08-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/10/15/2719 |
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| author | J. Alberto Conejero Jonathan Franceschi Enric Picó-Marco |
| author_facet | J. Alberto Conejero Jonathan Franceschi Enric Picó-Marco |
| author_sort | J. Alberto Conejero |
| collection | DOAJ |
| description | The concept of a fractional derivative is not at all intuitive, starting with not having a clear geometrical interpretation. Many different definitions have appeared, to the point that the need for order has arisen in the field. The diversity of potential applications is even more overwhelming. When modeling a problem, one must think carefully about what the introduction of fractional derivatives in the model can provide that was not already adequately covered by classical models with integer derivatives. In this work, we present some examples from control theory where we insist on the importance of the non-local character of fractional operators and their suitability for modeling non-local phenomena either in space (action at a distance) or time (memory effects). In contrast, when we encounter completely different nonlinear phenomena, the introduction of fractional derivatives does not provide better results or further insight. Of course, both phenomena can coexist and interact, as in the case of hysteresis, and then we would be dealing with fractional nonlinear models. |
| first_indexed | 2024-03-09T05:12:33Z |
| format | Article |
| id | doaj.art-fd66271332a64068bc16bcca1374a94a |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-09T05:12:33Z |
| publishDate | 2022-08-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-fd66271332a64068bc16bcca1374a94a2023-12-03T12:48:12ZengMDPI AGMathematics2227-73902022-08-011015271910.3390/math10152719Fractional vs. Ordinary Control Systems: What Does the Fractional Derivative Provide?J. Alberto Conejero0Jonathan Franceschi1Enric Picó-Marco2Instituto Universitario de Matemática Pura y Aplicada, Universitat Politècnica de València, 46022 Valencia, SpainDepartment of Mathematics “F. Casorati”, Università degli Studi di Pavia, 27100 Pavia, ItalyDepartamento de Ingeniería de Sistemas y Automática, Universitat Politècnica de València, 46022 Valencia, SpainThe concept of a fractional derivative is not at all intuitive, starting with not having a clear geometrical interpretation. Many different definitions have appeared, to the point that the need for order has arisen in the field. The diversity of potential applications is even more overwhelming. When modeling a problem, one must think carefully about what the introduction of fractional derivatives in the model can provide that was not already adequately covered by classical models with integer derivatives. In this work, we present some examples from control theory where we insist on the importance of the non-local character of fractional operators and their suitability for modeling non-local phenomena either in space (action at a distance) or time (memory effects). In contrast, when we encounter completely different nonlinear phenomena, the introduction of fractional derivatives does not provide better results or further insight. Of course, both phenomena can coexist and interact, as in the case of hysteresis, and then we would be dealing with fractional nonlinear models.https://www.mdpi.com/2227-7390/10/15/2719fractional-order modelfractional systemsnon-linear systemscomplex systemsstructural propertiesidentification for control process |
| spellingShingle | J. Alberto Conejero Jonathan Franceschi Enric Picó-Marco Fractional vs. Ordinary Control Systems: What Does the Fractional Derivative Provide? Mathematics fractional-order model fractional systems non-linear systems complex systems structural properties identification for control process |
| title | Fractional vs. Ordinary Control Systems: What Does the Fractional Derivative Provide? |
| title_full | Fractional vs. Ordinary Control Systems: What Does the Fractional Derivative Provide? |
| title_fullStr | Fractional vs. Ordinary Control Systems: What Does the Fractional Derivative Provide? |
| title_full_unstemmed | Fractional vs. Ordinary Control Systems: What Does the Fractional Derivative Provide? |
| title_short | Fractional vs. Ordinary Control Systems: What Does the Fractional Derivative Provide? |
| title_sort | fractional vs ordinary control systems what does the fractional derivative provide |
| topic | fractional-order model fractional systems non-linear systems complex systems structural properties identification for control process |
| url | https://www.mdpi.com/2227-7390/10/15/2719 |
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