From the solutions of diffusion equation to the solutions of subdiffusive one

Tadeusz Koszto owicz
2004 Journal of Physics A: Mathematical and General  
Starting with the Green's functions found for normal diffusion, we construct exact time-dependent Green's functions for subdiffusive equation (with fractional time derivatives), with the boundary conditions involving a linear combination of fluxes and concentrations. The method is particularly useful to calculate the concentration profiles in a multi-part system where different kind of transport occurs in each part of it. As an example, we find the solutions of subdiffusive equation for the
more » ... em composed from two parts with normal diffusion and subdiffusion, respectively.
doi:10.1088/0305-4470/37/45/005 fatcat:ctkalfnh4jhvxeinxibiywtsba