Diffusion equations with spatially dependent coefficients and fractal Cauer-type networks

TL;DR

This paper provides a comprehensive proof linking diffusion equations with spatially varying coefficients to fractal Cauer-type networks, expanding on prior work to clarify their mathematical relationship.

Contribution

It offers a self-contained proof establishing the connection between variable-coefficient diffusion equations and fractal Cauer-type networks, enhancing theoretical understanding.

Findings

Confirmed the mathematical relationship between diffusion equations and fractal networks

Clarified the theoretical foundation for fractional behavior modeling

Extended previous work with a detailed, self-contained proof

Abstract

We give a self-contained proof of the connection existing between diffusion equations with spatially dependent coefficients and fractal Cauer-type networks initiated by J. Sabatier in 2020 and discussed in more details in [J. Sabatier and al., Fractional behaviours modelling, Springer, 2022].