Anomalous Relaxation in Dielectrics with Hilfer Fractional Derivative
DOI:
https://doi.org/10.5890/JAND.2021.09.009Abstract
We introduce a new relaxation function depending on an arbitrary parameter as a solution of a kinetic equation in the same way as the relaxation function introduced empirically by Debye, Cole-Cole, Davidson-Cole and Havriliak-Negami regarding, anomalous relaxation in dielectrics, which are recovered as particular cases. We propose a differential equation introducing a fractional operator written in terms of the Hilfer fractional derivative of order $\xi$, with $0 < \xi \leq 1$ and type $\eta$, with $0 \leq \eta \leq 1$. To discuss the solution of the fractional differential equation, the methodology of Laplace transform is required. As a by product we mention particular cases where the solution is completely monotone. %Some graphics show the behaviour of this completely monotone function. Finally, the empirical models are recovered as particular cases.References
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