Fractional kinetics equation from a Markovian system of interacting Bouchaud trap models

We consider a partial exclusion process evolving on $\mathbb Z^d$ in a random trapping environment. In dimension $d\ge 2$, we derive the fractional kinetics equation \begin{equation*}\frac{\partial^βρ_t}{\partial t^β} = Δρ_t \end{equation*} as a hydrodynamic limit of the particle system. Here, $\f