Date of Award

Fall 2020

Document Type

Open Access Dissertation



First Advisor

Hong Wang


Variable-order fractional partial differential equations provide a competitive means in modeling challenging phenomena such as the anomalous diffusion and the memory effects and thus attract widely attentions. However, variable-order fractional models exhibit salient features compared with their constant-order counterparts and introduce mathematical and numerical difficulties that are not common in the context of integer-order and constant-order fractional partial differential equations.

This dissertation intends to carry out a comprehensive investigation on the mathematical analysis and numerical approximations to variable-order fractional derivative problems, including variable-order time-fractional, space-fractional, and space-time fractional partial differential equations, as well as the corresponding inverse problems. Novel techniques are developed to accommodate the impact of the variable fractional order and the proposed mathematical and numerical methods provide potential tools to analyze and compute the variable-order fractional problems.

Included in

Mathematics Commons