Mathematics, Department of


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A DISSERTATION Presented to the Faculty of The Graduate College at the University of Nebraska In Partial Fulfillment of Requirements For the Degree of Doctor of Philosophy Major: Mathematics Under the Supervision of Professor Allan C. Peterson Lincoln, Nebraska June, 2016

Copyright (c) 2016 Julia St. Goar


Boundary value problems have long been of interest in the continuous differential equations context. However, with the advent of new areas like Nabla Fractional Calculus, we may consider such problems in new contexts. In this work, we will consider several right focal boundary value problems, involving a Caputo fractional difference operator, in the Nabla Fractional Calculus context. Properties of the Green's functions for each of these boundary value problems will be investigated and, in the case of a particular boundary value problem, used to establish the existence of positive solutions to a nonlinear version of the boundary value problem.

Adviser: Allan C. Peterson

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