Date of Award


Document Type

Open Access Thesis




College of Arts and Sciences

First Advisor

Hong Wang


In physical point of view, relaxation usually describes the return from a perturbed system into equilibrium and each process has its own characteristic relaxation time. In 1946, Tool first formulated the notion of fictive temperature to characterize the structure of a glass-forming melt. Since then, people used to simulate structural relaxation by first order model. Since fractional-based models have not widely applied in modeling the fictive temperature, I want to explore the the possibility of modeling structural relaxation by fractional differential equation.

In this thesis, I will first introduce the definitions of two different kinds of fractional derivatives: Riemann-Liouville fractional derivative and Caputo fractional derivative briefly, and then show several existing and newly proposed models for structural relaxation and shape-memory behavior. Finally, I will illustrate the numerical scheme for each model and show some related numerical experiments.

Included in

Mathematics Commons