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 N -dimensional case into account. In our analysis, a spatial time-dependent diffusion coefficient is considered, i.e., D ( r , t ) = D t δ - 1 r - θ / Γ ( α ) . The presence of external forces F ( r ) = K r e with e = - 1 - θ and F ( r ) = - kr + K r e 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.