  The motion of contaminant particles through complex environments such as
fractured rocks or porous sediments is often characterized by anomalous
diffusion: the spread of the transported quantity is found to grow sublinearly
in time due to the presence of obstacles which hinder particle migration. The
asymptotic behavior of these systems is usually well described by fractional
diffusion, which provides an elegant and unified framework for modeling
anomalous transport. We show that pre-asymptotic corrections to fractional
diffusion might become relevant, depending on the microscopic dynamics of the
particles. To incorporate these effects, we derive a modified transport
equation and validate its effectiveness by a Monte Carlo simulation.
