A fractional partial differential equation is derived for the spreading of matter in a saturated porous medium starting from precise hypotheses concerning the medium itself, which is a collection of intertwisted tubes with randomly distributed slopes, filled with quiescent fluid. Examining the fundamental solution of the fractional equation indicates that the second moment is not proportional to time, which is the signature of anomalous diffusion. The equation derived preserves non-negativity and also the total mass of matter.