Conformable advection-dispersion models for radioactive waste migration: Robin-type condition and moment analysis

Within the framework of the conformable fractional-order derivative, conformable advection-dispersion models (CADMs) with Robin-type boundary conditions and different source terms are proposed to describe radioactive waste migration. Analytical solutions are derived using the conformable Laplace transform. The influence of the fractional derivative order on the concentration distribution and boundary concentration is illustrated graphically. Spatial moment analysis is conducted to evaluate the effectiveness of the proposed models for parameter estimation. Comparison with experimental data shows excellent agreement, indicating that the CADM with Robin-type boundary conditions characterizes radioactive waste migration more accurately. Furthermore, the generalized CADM exhibits greater flexibility and improved application potential compared with its corresponding integer-order model.