A unifying framework for generalised distributed-order fractional models

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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.