  In this paper we discuss some properties of linear fractional dispersive
waves. In particular, we compare the dispersion relations emerging from the
kinematic wave equation and from the linearised Korteweg - de Vries equation
with the corresponding time-fractionalized versions. For this purpose, we
evaluate the expressions for the phase velocity and for the group velocity,
highlighting the differences not only analytically, but also by means of
illuminating plots.
