  We consider a particle transport process in a one-dimensional system with a
thin membrane, described by a normal diffusion equation. We consider two
boundary conditions at the membrane that are linear combinations of integral
operators, with time dependent kernels, which act on the functions and their
spatial derivatives define on both membrane surfaces. We show how boundary
conditions at the membrane change the temporal evolution of the first and
second moments of particle position distribution (the Green's function) which
is a solution to normal diffusion equation. As these moments define the kind of
diffusion, an appropriate choice of boundary conditions generates the moments
characteristic for subdiffusion. The interpretation of the process is based on
a particle random walk model in which the subdiffusion effect is caused by
anomalously long stays of the particle in the membrane.
