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Sticky diffusion processes on bounded domains spend finite time (and finitemean time) on the lower-dimensional space given by the boundary. Once theprocess hits the boundary, then it starts again after a random amount of time.While on the boundary it can stay or move according to dynamics that aredifferent from those in the interior. Such processes may be characterized by atime-derivative appearing in the boundary condition for the governing problem.We use time changes obtained by right-inverses of suitable processes in orderto describe fractional sticky conditions and the associated boundarybehaviours. We obtain that fractional boundary value problems (involvingfractional dynamic boundary conditions) lead to sticky diffusions spending aninfinite mean time (and finite time) on a lower-dimensional boundary. Such abehaviour can be associated with a trap effect in the macroscopic point ofview.

Fractional Boundary Value Problems and elastic sticky Brownian motions, II: The bounded domain