  We propose the strongly tilted Bose-Hubbard model as a natural platform to
explore Hilbert-space fragmentation (HSF) and fracton dynamics in
two-dimensions, in a setup and regime readily accessible in optical lattice
experiments. Using a perturbative ansatz, we find HSF when the model is tuned
to the resonant limit of on-site interaction and tilted potential. First, we
investigate the quench dynamics of this system and observe numerically that the
relaxation dynamics strongly depends on the chosen initial state -- one of the
key signature of HSF. Second, we identify fractonic excitations with restricted
mobility leading to anomalous transport properties. Specifically, we find
excitations that show one dimensional diffusion (z = 1/2) as well as
excitations that show subdiffusive behaviour in two dimensions (z = 3/4). Using
a cellular automaton, we analyze their dynamics and compare to an effective
hydrodynamic description.
