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 ∂ α 1 P ( 0 + , t ) / ∂ t α 1 = ( D 1 / D 2 ) ∂ α 2 P ( 0 − , t ) / ∂ t α 2 , where the subdiffusion parameters α 1 , D 1 and α 2 , D 2 are defined in the regions x < 0 and x > 0 , respectively.