Fractional diffusion equation with an absorbent term and a linear external force: Exact solution

We investigate the solutions of a generalized diffusion equation which contains space and time fractional derivatives by taking an absorbent (or source) term and a linear external force into account. They are expressed in terms of the Fox H functions and, for some special cases, they are directly related to the Lévy distributions. We also analyze the first passage time distribution for the case characterized by the absence of absorbent (or source) term and external force for a semi-infinite interval with absorbent boundary conditions. We also discuss the connection of the results presented here with the anomalous diffusion.