Subdiffusion-absorption process in a system consisting of two different media.

Subdiffusion with reaction A+B→B is considered in a system which consists of two homogeneous media joined together; the A particles are mobile, whereas B are static. Subdiffusion and reaction parameters, which are assumed to be independent of time and space variables, can be different in both media. Particles A move freely across the border between the media. In each part of the system, the process is described by the subdiffusion-reaction equations with fractional time derivative. By means of the method presented in this paper, we derive both the fundamental solutions (the Green's functions) P(x, t) to the subdiffusion-reaction equations and the boundary conditions at the border between the media. One of the conditions demands the continuity of a flux and the other one contains the Riemann-Liouville fractional time derivatives ∂P(0,t)/∂t=(D/D)∂P(0,t)/∂t, where the subdiffusion parameters α, Dand α, Dare defined in the regions x<0 and x>0, respectively.