Journal of Physical Mathematics
- J. Phys. Math.
- Volume 6, Number 2 (2015), 7 pages.
Relaxation Equations: Fractional Models
The relaxation functions introduced empirically by Debye, Cole-Cole, Cole-Davidson and Havriliak-Negami are, each of them, solutions to their respective kinetic equations. In this work, we propose a generalization of such equations by introducing a fractional differential operator written in terms of the Riemann-Liouville fractional derivative of order $γ$, $0\ltγ\le1$. In order to solve the generalized equations, the Laplace transform methodology is introduced and the corresponding solutions are then presented, in terms of Mittag-Leffler functions. In the case in which the derivative’s order is $γ = 1$, the traditional relaxation functions are recovered. Finally, we presented some 2D graphs of these function.
J. Phys. Math., Volume 6, Number 2 (2015), 7 pages.
First available in Project Euclid: 31 August 2017
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Mittag-Leffler functions Laplace transform Riemann-Liouville derivative fractional differential equations dielectric relaxation complex susceptibility relaxation function response function Debye Cole-Cole Davidson-Cole Havriliak-Negami
CFAE, Rosa; E, Capelas de Oliveira. Relaxation Equations: Fractional Models. J. Phys. Math. 6 (2015), no. 2, 7 pages. doi:10.4172/2090-0902.1000146. https://projecteuclid.org/euclid.jpm/1504144903