G-Fractional Diffusion on Bounded Domains in <inline-formula><math display="inline"><semantics><msup><mi mathvariant="double-struck">R</mi><mi>d</mi></msup></semantics></math></inline-formula>

Abstract

In this paper, we study g-fractional diffusion on bounded domains in Rd with absorbing boundary conditions. A new general and explicit representation of the solution is obtained. 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.

Keywords

• fractional diffusion equation
• first-passage time
• <i>g</i>-fractional diffusion in bounded domain