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Sticky diffusion processes spend finite time (and finite mean time) on alower-dimensional boundary. Once the process hits the boundary, then it startsagain after a random amount of time. While on the boundary it can moveaccording to dynamics that are different from those in the interior. Suchprocesses may be characterized by a time-derivative appearing in the boundarycondition for the governing problem. We use time changes obtained byright-inverses of suitable processes in order to describe fractional stickyconditions and the associated boundary behaviors. We obtain that fractionalboundary value problems (involving fractional dynamic boundary conditions) leadto sticky diffusions spending an infinite mean time (and finite time) on alower-dimensional boundary. Such a behavior can be associated with a trapeffect in the macroscopic point of view.

Fractional Boundary Value Problems and Elastic Sticky Brownian Motions