First passage time distributions of anomalous biased diffusion with double absorbing barriers

We investigate the first passage time (FPT) problem of anomalous diffusion governed by the Galilei variant fractional diffusion-advection equation in the semi-infinite and finite domains subject to an absorbing boundary condition. We obtain explicit solutions for the FPT distributions and the corresponding Laplace transforms for both zero and constant drift cases by using the method of separation of variables as well as the properties of the Fox H function. An important relation between the FPT distributions corresponding to one and two absorbing barriers is revealed to determine the conditional FPT distributions. It shows that the proportion between the conditional FPT distributions only depends on the general Péclet number. We further discuss the asymptotic behavior of the FPT distributions and confirm our theoretical analysis by numerical results.