Non-Markovian diffusion equation and diffusion in a porous catalyst

We revisit the problem of diffusion in a porous catalyst by incorporating in the diffusion equation fractional time derivatives and a spatial dependent diffusion coefficient in order to extend the usual description to situations which have an unusual behavior. In our analysis, we also consider a nonlocal reaction term of linear order. We obtain exact solutions for the profile of substance in the porous catalyst in terms of the Green function approach. The results show an anomalous behavior of the concentration profile spreading which may be connected to anomalous diffusion.