2020 Virtual undergraduate Research symposium
Green’s Function for Fractional Nabla Boundary Value Problems
PROJECT NUMBER: 3
AUTHOR: Felix High, Applied Mathematics and Statistics
MENTOR: Areeba Ikram, Applied Mathematics and Statistics | MENTOR: Kevin Ahrendt, Applied Mathematics and Statistics
ABSTRACT
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A discrete boundary value problem (BVP) looks at a problem with boundary conditions in a discrete setting. We examine the general solution of a discrete fractional nabla difference equation. Then, we consider a BVP involving the equation with Robin and Sturm-Liouville boundary conditions. We then derive the Green’s function from the general solution and given conditions.
VISUAL PRESENTATION
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AUTHOR BIOGRAPHY
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Felix is a current senior at mines, graduating December 2020 with a major in Computational and Applied Mathematics and a minor in Computer Science. He’s worked on research in discrete nabla fractional calculus for the past couple years. Prior to this project, he worked on nabla trigonometric identities. For future research, he wants to move towards other math topics such as analysis, topology, or algebra.
This looks like very competent work, but the presentation is frankly too hairy for this nonmathematician. In particular, you give no motivation for doing the work. Why is anyone interested in a fractional derivative? I will take your word for the equations in the lower left, but what is v? H? You say mu may be any real value; does it have to be less than 1? When you finally get the Green’s functions, what is their significance? Why the big drops; do they make intuitive sense? (Incidentally, a quibble: Functions are usually denoted by curves and experimental data by points. By that standard the Green’s functions should have been denoted by curves, unless you had some reason to want to single out the individual points.) “Future Research” is good, but it is not a conclusion. The poster, despite the evident high quality of the work, lacks a clear introduction, a motivation, and a summary or conclusion, and it is not really accessible to the nonspecialist.