We study the dynamical properties of the one dimensional XXZ model at infinite temperature in the presence of quench disorder. This model is expected to exhibit a many body localization (MBL) transition at finite disorder. We compute the local dynamical spin correlation function using a non-perturbative continued fraction expansion. The expansion up to 15th order is sufficient to achieve convergence of our extrapolation scheme. We compare the continued fraction result to the exact diagonalization (ED) on 22 sites. The phase diagram is determined in the disorder-anisotropy plane. Our main finding is the emergence of sub-diffusive transport and absence of a diffusive behavior (ω^-1/2 at low frequencies) in the weak disorder regime. The lack of a true diffusive phase contrasts with previous results and expectations obtained from smaller system sizes. In addition, the MBL transition is determined to occur at lower values than those deduced by ED on finite systems.