A note on fractional-order derivatives of periodic functions

✍ Scribed by Mohammad Saleh Tavazoei

• Publisher: Elsevier Science
• Year: 2010
• Tongue: English
• Weight: 393 KB
• Volume: 46
• Category: Article
• ISSN: 0005-1098
• DOI: 10.1016/j.automatica.2010.02.023

✦ Synopsis

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.