Fractional diffusion equations interpolate between damping and waves
Mathematical Physics
2024-10-14 v1 Statistical Mechanics
High Energy Physics - Theory
math.MP
Abstract
The behaviour of the solutions of the time-fractional diffusion equation, based on the Caputo derivative, is studied and its dependence on the fractional exponent is analysed. The time-fractional convection-diffusion equation is also solved and an application to Pennes bioheat model is presented. Generically, a wave-like transport at short times passes over to a diffusion-like behaviour at later times.
Cite
@article{arxiv.2403.04887,
title = {Fractional diffusion equations interpolate between damping and waves},
author = {Andy Manapany and Sébastien Fumeron and Malte Henkel},
journal= {arXiv preprint arXiv:2403.04887},
year = {2024}
}