On G-fractional diffusion models in bounded domains

TL;DR

This paper investigates g-fractional diffusion equations in bounded domains, providing explicit solutions and analyzing first passage times, revealing conditions for finite mean first-passage times unlike classical fractional diffusion.

Contribution

It introduces explicit solutions for g-fractional diffusion with absorbing boundaries and demonstrates how specific functions g can yield finite MFPTs, advancing understanding of anomalous diffusion models.

Findings

Explicit solution for g-fractional diffusion in bounded domains.

Identification of conditions for finite mean first-passage time.

Comparison with classical fractional diffusion showing differences in MFPT.

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 $g$ it is possible to obtain a finite MFPT, differently from the anomalous diffusion described by a fractional heat equation involving the classical Caputo derivative.