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.
"Relaxation Equations: Fractional Models." J. Phys. Math. 6 (2) 1 - 7, 2015. https://doi.org/10.4172/2090-0902.1000146