We introduce a new relaxation function depending on an arbitrary parameter as solution of a kinetic equation in the same way as the relaxation function introduced empirically by Debye, Cole-Cole, Davidson-Cole and Havriliak-Negami, 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 ξ, with 0 < ξ ≤ 1 and type η, with 0 ≤ η ≤ 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.Finally, the empirical models are recovered as particular cases.