Subdiffusion in a system with a partially permeable partially absorbing wall

We consider subdiffusion of a particle in one-dimensional system with thin partially permeable wall. Passing through the wall, can be absorbed certain probability. call such wall absorbing (PPAW). Using diffusion model discrete time and spatial variable, probability densities (Green's functions) describing have been derived. Knowing Green's functions we derive boundary conditions at The take specific form which derivatives fractional order controlled by parameter are involved. assume that absorption occur only when jumps It is not possible to temporarily retain inside represent membrane. If thick membrane particles may diffuse considered, it treated as three-part middle part. surfaces assumed for PPAW. PPAW used filter diffusing particles. temporal evolution molecule has considered. This function shows efficiency filtering process. impact parameters on this discussed.