Project Info
Exploring Discrete Fractional Calculus
Areeba Ikram | aikram@mines.edu
Students are familiar with the concept of a derivative from calculus, but what does it mean to take a half or pi-th order derivative? Discrete fractional calculus addresses this idea in the setting of functions defined on a discrete domain. The goals of this project are to extend ideas that students have learned in calculus and differential equations in the case of fractional differences in place of ordinary derivatives. In particular, trigonometric and exponential functions in the discrete fractional context and their properties and fractional differences will be further explored. Moreover, applications and modeling using fractional difference equations can be explored.
More Information
Discrete Fractional Calculus by Goodrich and Peterson
Grand Engineering Challenge: Not applicable
Student Preparation
Qualifications
The student should have taken at minimum Calculus 1 and 2, and differential equations, but more experience in coursework is preferred. Intro to Proofs, in particular, is a preferred prerequisite course.
Time Commitment
16-24 hours/month
Skills/Techniques Gained
Students will apply skills from calculus courses in the new setting of discrete fractional calculus. Students will learn techniques for exploring original ideas in mathematics.
Mentoring Plan
We will meet at least once a week for about an hour. In these meetings, we will discuss what the student has tried and discovered in the previous week and address any problems that arise. Then, we will set tasks to complete and problems to attempt for the following week. Weekly progress and tasks will be recorded in an ongoing document. The student will keep an ongoing typed record of work on the project.