Continuous Medium Model for Fractal Media

TL;DR

This paper develops a fractional calculus-based model to describe fractal media with noninteger mass dimensions, generalizing classical equations for mass and continuity.

Contribution

It introduces fractional integral formulations for media with fractal structures, extending traditional models to account for noninteger mass dimensions.

Findings

Fractional integrals effectively describe fractal media.

Derived fractional generalizations of mass and continuity equations.

Validated the applicability of fractional calculus to fractal media.

Abstract

We consider the description of the fractal media that uses the fractional integrals. We derive the fractional generalizations of the equation that defines the medium mass. We prove that the fractional integrals can be used to describe the media with noninteger mass dimensions. The fractional equation of continuity is considered.