Fractional diffusion equation and Green function approach: Exact solutions

We investigate the solutions of a fractional diffusion equation with radial symmetry by using the Green function approach and by taking the NN-dimensional case into account. In our analysis, a spatial time-dependent diffusion coefficient is considered, i.e., D(r,t)=Dtδ-1r-θ/Γ(α)D(r,t)=Dtδ-1r-θ/Γ(α). The presence of external forces F(r)=KrεF(r)=Krε with ε=-1-θε=-1-θ and F(r)=-kr+KrεF(r)=-kr+Krε is also taken into account. In particular, we discuss the results obtained by employing boundary conditions defined on a finite interval, and afterwards the analysis is extended to a semi-infinite interval. Finally, we also discuss a rich class of diffusive processes that can be obtained from the results presented in this work.