Fractional diffusion models for radionuclide anomalous transport in geological repository systems

Using the new derivatives of fractional order, alluded to the Atangana-Baleanu (AB) derivative and Caputo-Fabrizio (CF) derivative, three fractional diffusion models are proposed to describe radionuclide anomalous transport in geological repository systems. The analytical solutions of the Atangana-Baleanu fractional diffusion (ABFD) models and Caputo-Fabrizio fractional diffusion (CFFD) model in the context of instantaneous and constant concentration source are presented. The mean square displacements (MSDs) for the ABFD and CFFD models in terms of instantaneous source are investigated. Based on the fitting analysis of experimental data of radionuclide diffusion, parameters related to the ABFD and CFFD models are determined. The good agreement between the theoretical and experimental results indicates that the proposed fractional diffusion models are more effective and flexible to characterize the radionuclide anomalous migration. Furthermore, the comparison of the proposed ABFD and CFFD models is also discussed.