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 Professors Lynn Erbe and Allan Peterson. Lincoln, Nebraska: August, 2012

Copyright (c) 2012 Christopher S. Goodrich


In this work we provide an analysis of both fractional- and integer-order boundary value problems, certain of which contain explicit nonlocal terms. In the discrete fractional case we consider several different types of boundary value problems including the well-known right-focal problem. Attendant to our analysis of discrete fractional boundary value problems, we also provide an analysis of the continuity properties of solutions to discrete fractional initial value problems. Finally, we conclude by providing new techniques for analyzing integer-order nonlocal boundary value problems.

Adviser: Lynn Erbe and Allan Peterson