Project Info
Modeling in Discrete Fractional Calculus
Kevin Ahrendt | kahrendt@mines.edu
Discrete fractional calculus has only recently been studied in detail and has many open questions to research. It has been shown that differential equation models involving fractional derivatives describe certain physical phenomena better than traditional whole-order differential equation models. We will develop tools to fit data to fractional difference equations with real world data to see if we can better predict outcomes in comparison to traditional models.
More Information
“Discrete Fractional Calculus” by Goodrich and Peterson provides a self-contained introduction to the area. The paper “Modeling with fractional difference equations” by Atici and Eloe gives a model of tumor growth using fractional differences.
Grand Engineering Challenge: Not applicable
Student Preparation
Qualifications
Successful completion of Math 225 (Differential Equations) and Math 300 (Foundations of Advanced Mathematics).
Time Commitment
16-24 hours/month
Skills/Techniques Gained
Students will learn a new area of mathematics that has many open questions that can be easily accessed. They will experience the process of original mathematical research and how to approach unsolved problems.
Mentoring Plan
In the fall semester, we will work through a foundational textbook to build up background material. This will be accomplished with weekly meetings to discuss sections of the textbook along with exercises to ensure an active understanding. In the spring semester, we will continue meeting weekly but with the focus on open problems in the area, including taking real world data and attempting to fit it to fractional difference equations.