  A microscopic model in the framework of fractional kinetics to describe
spatial dispersion of power-law type is suggested. The Liouville equation with
the Caputo fractional derivatives is used to obtain the power-law dependence of
the absolute permittivity on the wave vector. The fractional differential
equations for electrostatic potential in the media with power-law spatial
dispersion are derived. The particular solutions of these equations for the
electric potential of point charge in this media are considered.
