Sturm-Liouville Problems in Discrete Nabla Fractional Calculus

PROJECT NUMBER: 4

AUTHOR: Rocco Marchitto, Applied Mathematics and Statistics | MENTOR: Kevin Ahrendt, Applied Mathematics and Statistics

ABSTRACT

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We consider a discrete nabla fractional Sturm-Liouville boundary-value problem in the Caputo sense. We prove basic properties of the system including existence of solutions and develop analytical approximations to the system solutions. Furthermore, eigenvalue results analogous to continuous classical Sturm-Liouville systems are introduced and developed. Finally, we expound computational aspects and develop illustrations of sample solutions to the system.

VISUAL PRESENTATION

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AUTHOR BIOGRAPHY

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Rocco Marchitto is a junior at the Colorado School of Mines. He is majoring in computational and applied mathematics. He is currently researching the field of discrete fractional calculus, a new and interesting area of mathematics with applications in science and engineering, and is interested in finding interesting connections between abstract mathematical theory and practical applications.

Sponsored by Phillips 66