Magnetohydrodynamics of Fractal Media

TL;DR

This paper develops a fractional calculus framework to describe magnetohydrodynamics in media with fractal structures, focusing on charged particle distributions and turbulent media with fractal features.

Contribution

It introduces a fractional integral approach to extend magnetohydrodynamics equations for fractal media, providing a new theoretical foundation.

Findings

Derived magnetohydrodynamics equations for fractal media

Analyzed equilibrium states of the fractional equations

Proposed fractional integrals as approximations on fractals

Abstract

The fractal distribution of charged particles is considered. An example of this distribution is the charged particles that are distributed over fractal. The fractional integrals are used to describe fractal distribution. These integrals are considered as approximations of integrals on fractals. Typical turbulent media could be of a fractal structure and the corresponding equations should be changed to include the fractal features of the media. The magnetohydrodynamics equations for fractal media are derived from the fractional generalization of integral Maxwell equations and integral hydrodynamics (balance) equations. Possible equilibrium states for these equations are considered.