A fractional diffusion equation with sink term

Approaching dynamical aspects in systems with localised sink term is fundamentally relevant from the physical-experimental point of view. However, theoretical advances have not progressed much in this direction; this is due to the great difficulty of addressing such types of problems from an analytic point of view. In this work, we investigate the systems sink points (like traps) considering a dynamics governed by the like reaction–diffusion equation in the presence of fractional derivatives. In order to do so, making use of the continuous-time random walks theory we constructed a model that contains multiples sink terms, on sequence we analysed the problem for two cases: first, considering only a single sink term and, second, considering multiples sink point associated with a fractal set. In both cases, we present the analytic solution in terms of Fox and Mittag–Leffler functions. Moreover, we perform a calculus of the mean square displacement and survival probability. The proposal and the techniques used in this work are useful to describe anomalous diffusive phenomena and the transport of particles in irregular media.