Subdiffusion in a system with a thick membrane

We theoretically study subdiffusion in a system, in which homogeneous thick membrane separates two media; in each of them there are different subdiffusion parameters. Subdiffusion is described by the linear differential equations with fractional time derivative and the boundary conditions requiring that the ratio of substance concentrations on both sides of the membrane surface is constant in time. Starting with the Green’s functions derived for the considered system, we discuss the property of the concentrations found in the long time limit for the system where initially the membrane separates pure solvent from homogeneous solution.