Fractional order derivatives in circuit theory

What is it about?

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 fractional order differential equation

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