Fractional power-law spatial dispersion in electrodynamics

•Plasma-like non-local media with power-law spatial dispersion.•Fractional differential equations for electric fields in the media.•The generalizations of Coulomb’s law and Debye’s screening for the media.

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.