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A note on fractional-order derivatives of periodic functions
Tavazoei, M. S ; Sharif University of Technology | 2010
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- Type of Document: Article
- DOI: 10.1016/j.automatica.2010.02.023
- Publisher: 2010
- Abstract:
- In this paper, it is shown that the fractional-order derivatives of a periodic function with a specific period cannot be a periodic function with the same period. The fractional-order derivative considered here can be obtained based on each of the well-known definitions Grunwald-Letnikov definition, Riemann-Liouville definition and Caputo definition. This concluded point confirms the result of a recently published work proving the non-existence of periodic solutions in a class of fractional-order models. Also, based on this point it can be easily proved the absence of periodic responses in a wider class of fractional-order models. Finally, some examples are presented to show the applicability of the paper achievements in the solution analysis of fractional-order systems
- Keywords:
- Fractional-order derivative ; Fractional calculus ; Fractional-order systems ; Non-existence ; Periodic function ; Periodic response ; Periodic solution ; Solution analysis ; Calculations ; Problem solving
- Source: Automatica ; Volume 46, Issue 5 , May , 2010 , Pages 945-948 ; 00051098 (ISSN)
- URL: http://www.sciencedirect.com/science/article/pii/S0005109810000956