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Diffusion problem with a specification of considering liquid redistribution  from a thin interlayer between two semi-infinite media in contact is  developed. The basic approach involves an integral approach defining finite  depths of penetration of the diffusant into the media and fractional  half-time derivative of the boundary (at the interface) concentration. The  approach is straightforward and avoids cumbersome calculations based on the  idea to develop entire domain (for each of the contacting bodies) solutions.  The results are compared to classical solutions, when they exist

Redistribution of mass from a thin interlayer between two thick dissimilar media: 1-D diffusion problem with a non-local condition