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

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.