A unifying framework for generalised distributed-order fractional models

该项目旨在利用测量理论和一类新的分布阶非局部算子为广义分数模型建立一个统一的理论框架，以模拟非均质和各向异性多孔介质中的异常输运过程。该项目希望为分数建模和现代实践中使用的分数算子的许多变体的作用和关系的清晰度以及如何在有限域上施加边界条件提供数学基础。该项目的预期成果包括评估分数输运模型中控制方程的维数和/或复杂性降低，重点是地下水应用。

This project aims to develop a unifying theoretical framework for generalised fractional models using measure theory and a new class of distributed-order nonlocal operators to simulate anomalous transport processes in heterogeneous and anisotropic porous media. The project expects to generate a mathematical foundation for fractional modelling and clarity on the role of, and relationship between, the many variants of fractional operators used in modern practice and how to impose boundary conditions on finite domains. Expected outcomes of the project include an evaluation of dimensionality and/or complexity reduction of the governing equations in fractional transport models with a focus on groundwater applications.