Development of a novel best approximation theory with applications

本课题旨在建立具有不连续性和非紧性的复杂分数阶边值问题的最佳逼近理论，并应用该理论研究两类具有工业应用的复杂偏微分方程边值问题。这项工作将导致一种新的理论和一套创新的分析和计算方法的发展，用于解决各种具有奇点和非局部性质的非线性问题。该项目的预期结果将显著推进我们对许多工业系统和过程的建模和控制方法。

The aim of this project is to develop an innovative best approximation theory for complex fractional boundary value problems with discontinuities and with no compactness, and then apply the theory to study two classes of complex partial differential equation boundary value problems with industrial applications. The work will lead to the development of a new theory and a suite of innovative analytical and computational methods for solving a wide range of nonlinear problems with singularities and non-local properties. The expected outcomes of the project will significantly advance our methods for the modelling and control of many industrial systems and processes.