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The strength and dilatancy of sand are mainly influenced by the void ratio, confining pressure and stress path. In engineering, the stress-strain relationship of sand in three-dimensional stress state is complicated, where the state-dependent properties of sand are difficult to be described by traditional constitutive models. Thus, fractional plastic models based on different fractional derivatives were developed to capture such state-dependent behavior of sand. This paper attempts to make a comparative study of the fractional models based on two typical fractional derivatives, i.e., the R-L derivative and Caputo derivative. The results show that the different types of fractional derivatives are mainly reflected in the different order of differentiation and integration, which will have a significant impact on the calculation of plastic flow direction, stress-dilatancy ratio and fractional order parameter β in the constitutive model. By determining the constitutive parameters of the two models, the constitutive behaviors predicted by different models were compared with the corresponding test results of saturated sands under different initial mean pressures and different stress paths. The models can reasonably simulate the test results of saturated sands, where the dilatancy characteristic can be captured. Compared with R-L model, Caputo model can predict more volumetric strain in the dilatancy process, and has better prediction effect. Overall, the predicted effects of the two models are close, with a maximum difference of about 7 %. • Fractional plastic models based on different fractional derivatives were developed. • Two typical fractional derivatives are compared between R-L and Caputo derivative. • Stress-dilatancy relationship for different types of fractional order models were analyzed. [ABSTRACT FROM AUTHOR]