Solute transport in soils and sediments is commonly simulated with the parabolic advective-dispersive equation, or ADE, that can be derived assuming solute particles undergo Brownian motion. Recently, a new model was proposed that assumes that the movement of solute particles belongs to the family of Lévy motions. A one-dimensional solute transport equation was derived for Lévy motions using fractional derivatives to describe the dispersion. Our objective was to test applicability of this fractional ADE, or FADE, to soils. We evaluated the FADE as the transport model in comparison with ADE with data from published miscible displacement experiments. The FADE, as a general model that included ADE, accurately simulated experimental breakthrough curves. Of the 53 experiments considered, 28 were fitted better with Lévy parameter smaller than two, i.e. with the fractional model, and 25 have been best fitted with the Lévy parameter equal to two, i.e. with the classical ADE model. This suggested that FADE rather than ADE could be used as a general framework to study solute transport in soil. The Lévy parameter varied with solute transport experimental conditions, i.e. type of soil, type of tracer, flow velocity and saturation degree. These differences presumably reflected different degrees of complexity in the movement of solute particles in soil that might be caused by the differences in the hierarchical structure of soil pore space for each particular case. Trends of the increase in the Lévy parameter values with the increase in saturation and in flow velocity were been observed. The fractional advective-dispersive equation as a generalization of classical advective-dispersive equation is a promising enhancement of the soil hydrology toolbox.