The application of hypergeometric functions to computing fractional order derivatives of sinusoidal functions

• Autorzy: Włodarczyk M. , Zawadzki A.

Identyfikatory

DOI

10.1515/bpasts-2016-0026

• Języki publikacji: EN

Abstrakty

EN

In the paper, the analytical forms of fractional order derivatives of sinusoidal function according to definitions of Riemann - Liouville and Caputo are presented. To determine the analytical form of the integrals appearing in definitions of derivatives of fractional order the Lommel functions from hypergeometrical functions family were applied. With the use of properties of the derivatives of fractional order - differential-integral there were presented the conception of generalized element of a single equation, which depending on the value of the derivative order, can be inductor, resistor, capacitor, or a hypothetical element of a fractional order differential equation.

Słowa kluczowe

EN

fractional degree derivative; hypergeometric function; Lommel function

PL

pochodna ułamkowa; funkcja hipergeometryczna; funkcja Lommela

• Wydawca: Polska Akademia Nauk, Wydział IV Nauk Technicznych
• Czasopismo: Bulletin of the Polish Academy of Sciences. Technical Sciences
• Rocznik: 2016
• Tom: Vol. 64, nr 1
• Strony: 243--248
• Opis fizyczny: Bibliogr. 25 poz., wykr.

Twórcy

autor

Włodarczyk M.

• Faculty of Electrical Engineering, Automatic Control and Computer Science, Kielce University of Technology, 7 Tysiąclecia Państwa Polskiego Ave., 25-314 Kielce, Poland

autor

Zawadzki A.

• Faculty of Electrical Engineering, Automatic Control and Computer Science, Kielce University of Technology, 7 Tysiąclecia Państwa Polskiego Ave., 25-314 Kielce, Poland

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