Abstract
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 \(\alpha\) 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.
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The datasets used and analysed during the current study available from the corresponding author on reasonable request.
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The funding sources are greatly acknowledged. The authors really appreciate the editors and anonymous reviewers for their valuable and constructive suggestions, which have greatly contributed to the improvement of this work.
Funding
This work was funded by the National Natural Science Foundation of China (52574121, 52504102, 52204110), Deep Earth Probe and Mineral Resources Exploration-National Science and Technology Major Project (2024ZD1003902), Intergovernmental International Science and Technology Innovation Cooperation Key Special Project (2025YFE0109800), European Commission Horizon Europe Marie Skłodowska-Curie Actions Staff Exchanges Project-LOC3G (101129729).
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Qing Wei: Methodology, Investigation,Validation, Software, Writing-original draft preparation. Shuai Yang: Conceptualization, Writing-original draft preparation, Writing-review and editing, Supervision. Senlin Xie: Validation, Investigation, Supervision.
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Wei, Q., Yang, S. & Xie, S. Conformable advection-dispersion models for radioactive waste migration: Robin-type condition and moment analysis. Sci Rep (2026). https://doi.org/10.1038/s41598-026-47478-7
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DOI: https://doi.org/10.1038/s41598-026-47478-7
