Continuous Time Random Walks with Internal Dynamics and Subdiffusive   Reaction-Diffusion Equations
  We formulate the generalized master equation for a class of continuous time random walks in the presence of a prescribed deterministic evolution between successive transitions. This formulation is exemplified by means of an advection-diffusion and a jump-diffusion scheme. Based on this master equation, we also derive reaction-diffusion equations for subdiffusive chemical species, using a mean field approximation. 
S. Eule, R. Friedrich, F. Jenko, and I. M. Sokolov