# Power-law Spatial Dispersion from Fractional Liouville Equation

Source: [Power-law Spatial Dispersion from Fractional Liouville Equation](<https://www.sota2.com/research/paper/68fa2e5f1e209131ce861e04>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-28T13:53:26.721Z

Authors: Vasily E. Tarasov

Published: 2013-07-18T13:09:31.000Z

## Abstract

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.

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/1307.4930>)

[PDF](<https://arxiv.org/pdf/1307.4930.pdf>)