G-fractional diffusion on bounded domains in $\mathbb{R}^d$

TL;DR

This paper investigates g-fractional diffusion processes on bounded domains, providing explicit solutions, analyzing first passage times, and connecting the theory to fractional Dodson diffusion models in physics.

Contribution

It offers an explicit representation of solutions for g-fractional diffusion with absorbing boundaries and explores the impact of the function g on first passage times, including applications to physical models.

Findings

Explicit solution representations for g-fractional diffusion.

Dependence of first passage time distribution on g.

Application to fractional Dodson diffusion model.

Abstract

In this paper we study $g$-fractional diffusion on bounded domains in $\mathbb{R}^d$ with absorbing boundary conditions. We show the explicit representation of the solution and then we study the first passage time distribution, showing the dependence on the particular choice of the function $g$. Then, we specialize the analysis to the interesting case of a rectangular domain. Finally we briefly discuss the connection of this general theory with the physical application to the so-called fractional Dodson diffusion model recently discussed in the literature.