On G-fractional diffusion models in bounded domains
Abstract
In the recent literature, the g-subdiffusion equation involving Caputo fractional derivatives with respect to another function has been studied in relation to anomalous diffusions with a continuous transition between different subdiffusive regimes. In this paper we study the problem of g-fractional diffusion in a bounded domain with absorbing boundaries. We find the explicit solution for the initial-boundary value problem and we study the first passage time distribution and the mean first-passage time (MFPT). An interestin outcome is the proof that with a particular choice of the function it is possible to obtain a finite MFPT, differently from the anomalous diffusion described by a fractional heat equation involving the classical Caputo derivative.
Cite
@article{arxiv.2209.11161,
title = {On G-fractional diffusion models in bounded domains},
author = {L. Angelani and R. Garra},
journal= {arXiv preprint arXiv:2209.11161},
year = {2023}
}
Comments
Accepted by Phys. Rev. E