  Electric fields in non-local media with power-law spatial dispersion are
discussed. Equations involving a fractional Laplacian in the Riesz form that
describe the electric fields in such non-local media are studied. The
generalizations of Coulomb's law and Debye's screening for power-law non-local
media are characterized. We consider simple models with anomalous behavior of
plasma-like media with power-law spatial dispersions. The suggested fractional
differential models for these plasma-like media are discussed to describe
non-local properties of power-law type.
