The Theory of Discrete Fractional Calculus: Development and Application

Authors

Michael T. Holm, University of Nebraska-LincolnFollow

First Advisor

Lynn Erbe

Second Advisor

Allan Peterson

Date of this Version

Spring 4-2011

Comments

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: May, 2011
Copyright 2011 Michael Holm

Abstract

The author's purpose in this dissertation is to introduce, develop and apply the tools of discrete fractional calculus to the arena of fractional difference equations. To this end, we develop the Fractional Composition Rules and the Fractional Laplace Transform Method to solve a linear, fractional initial value problem in Chapters 2 and 3. We then apply fixed point strategies of Krasnosel'skii and Banach to study a nonlinear, fractional boundary value problem in Chapter 4.

Adviser: Lynn Erbe and Allan Peterson