In this talk I will introduce a new interacting particle system consisting of interacting random walks in a trapping environment, known as Bouchaud trap models.
I will show that the hydrodynamic equation emerging from such system is the Fractional Kinetics Equation, a sub-diffusive PDE.

Based on a ongoing project with A. Chiarini (Padova), F. Redig (Delft) and F. Sau (Trieste).