A unifying framework for generalised distributed-order fractional models

广义分布式阶分数模型的统一框架

• 批准号: DP180103858
• 负责人: Prof Ian Turner
• 金额: $ 25.49万
• 依托单位: Queensland University of Technology
• 依托单位国家: 澳大利亚
• 项目类别: Discovery Projects
• 财政年份: 2018
• 资助国家: 澳大利亚
• 起止时间: 2018-05-17 至 2021-12-31
• 项目状态: 已结题
• 来源: https://dataportal.arc.gov.au/RGS/Web/Grants/DP180103858
• 关键词: unifying; framework; generalised; distributed; order

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.

该项目旨在为广义分数模型开发一个统一的理论框架，使用测度理论和一类新的分布阶非局部算子来模拟非均质和各向异性多孔介质中的异常输运过程。该项目预计将产生分数建模和清晰的作用的数学基础，以及现代实践中使用的分数算子的许多变体之间的关系，以及如何在有限域上施加边界条件。该项目的预期成果包括评价分数迁移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。