Subdiffusion-absorption process in a system consisting of two different media separated by a thin membrane

We consider normal diffusion, subdiffusion and slow subdiffusion in a system which consists of two media separated by a thin membrane. The subdiffusion and absorption parameters may be different in each of the medium. Using the new method we derive the probabilities describing a particle's random walk in the system. Within this method we firstly consider the particle's random walk in a system with both discrete time and space variables. Then, we move from discrete to continuous variables. The presented method provides differential-integral equations describing various processes of anomalous diffusion with absorption. Some of the equations are interpreted as fractional differential equations. From the obtained probabilities, we derive the boundary conditions at the membrane. We also show the biological applications of the model.