Development of a novel best approximation theory with applications

本项目的目的是发展一种新的最佳逼近理论来解决具有间断和非紧性的复分数次边值问题，并将该理论应用于研究两类具有工业应用的复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，以解决具有奇异性和非局部性质的广泛的非线性问题。该项目的预期结果将极大地改进我们用于许多工业系统和过程的建模和控制的方法。

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.