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Solute dispersivity in the conventional advective-dispersive equation (ADE) was found to increase with a distance from the source. This can be explained assuming 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. The FADE has two parameters - the fractional dispersion coefficient and the order of fractional differentiation α, 0<α<2. Scale effects are reflected by the value of α, and the fractional dispersion coefficient is independent on scale. The ADE is a special case of the FADE. Analytical solutions of the FADE and the ADE were successfully fitted to the data from field experiments on chloride transport in sandy loam and clay loam soils. The FADE simulated scale effects on solute transport better than ADE.