Generalised polynomial chaos approximation for stochastic fractional partial differential equations - Teh, Yu Xuan (Nanyang Technological University, 2023)
Fractional diffusion equations are widely used in various fields, such as physics, chemistry, biology, finance, and economics, to model the spread of particles, diseases, and financial variables. It is characterized by the anomalous diffusion of particles, which occurs in a non-Gaussian and non-local manner. However, solving these equations is a challenging task due to the non-local nature of the fractional Laplacian operator on a bounded domain. To address this issue, this thesis studies the Caffarelli-Stinga extension problems of the fractional diffusion equations, which localises the non-local operator on a semi-infinite cylinder.