Regularity for solutions of non local parabolic equations II
  We prove boundary regularity and a compactness result for parabolic nonlocal equations of the form $u_t-Iu=f$, where the operator $I$ is not necessarily translation invariant. As a consequence of this and the regularity results for translation invariant case, we obtain $C^{1,\alpha}$ interior estimates in space for non translation invariant operators under some hypothesis on the time regularity of the boundary data. 
Hector A. Chang Lara and Gonzalo Davila
math.AP