Spatial behavior of anomalous transport

We present a general derivation of one-dimensional spatial concentration distributions for anomalous transport regimes. Such transport can be captured in the framework of a continuous time random walk with a broad transition time distribution. This general theory includes a Fokker-Planck equation as a particular limiting case. All of the concentration profiles, as well as the associated temporal first passage time distributions, can be written in terms of a single special function (that belongs to the class of Fox functions). In addition, we consider the first two moments of the spatial concentration distributions, and determine not only their scaling behavior with time but also the coefficients and correction terms.