Diffusion-Weighted (DW) imaging has a monoexponential signal decay at low b-values related to the statistical mechanics of Brownian motion. However, at high b-values the DW signal is no longer monoexponential. Various models have been proposed to better fit the data; nevertheless, none of them assumes that the DW signal is governed by the fractional-time order dynamics of the generalized Brownian motion (a.k.a., anomalous diffusion). In this work, by assuming anomalous diffusion we solve the fractional-time order Bloch-Torrey equation for smooth diffusion-weighting gradients and compare the obtained model to existing ones. The proposed model outperforms state-of-the-art on synthetic anomalous phantom experiments.