# On spherically symmetrical accretion in fractal media

## TL;DR

This paper extends the classical theory of spherical accretion to fractal media using fractional calculus, revealing how accretion rates and dependencies on central mass differ in fractal environments, aligning with observations and simulations.

## Contribution

It introduces a fractional continuous medium model for spherical accretion in fractal media, generalizing the Bondi solution to account for fractal dimensionality.

## Key findings

- Accretion rates can vary significantly in fractal media.
- Dependence on central mass changes with fractal dimensionality.
- Model aligns with observational and simulation data for star accretion.

## Abstract

We use fractional integrals to generalize the description of hydrodynamic accretion in fractal media. The fractional continuous medium model allows the generalization of the equations of balance of mass density and momentum density. These make it possible to consider the general case of spherical hydrodynamic accretion onto a gravitating mass embedded in a fractal medium. The general nature of the solution is similar to the "Bondi solution", but the accretion rate may vary substantially and the dependence on central mass may change significantly depending on dimensionality of the fractal medium. The theory shows consistency with the observational data and numerical simulation results for the particular case of accretion onto pre-main-sequence stars.