  A modification of the Drude dispersive model based on fractional time
derivative is presented. The dielectric susceptibility is calculated
analytically and simulated numerically, showing a good agreement between
theoretical description and numerical results. The absorption coefficient and
wave vector -- key parameters describing the propagation of waves in such a
medium -- are shown to follow a power law in the frequency domain, which is a
common phenomenon in many real life applications. The introduction of two
separate parameters provides a more flexible model than some other approaches
found in literature and is well suited for numerical implementation.
