The Theory of Discrete Fractional Calculus: Development and Application

The author\u27s 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\u27skii and Banach to study a nonlinear, fractional boundary value problem in Chapter 4. Adviser: Lynn Erbe and Allan Peterso