Publication Date

Fall 2019

Advisor(s) - Committee Chair

Dr. Ferhan Atici (Director), Dr. Mark Robinson, and Dr. John Spraker

Degree Program

Department of Mathematics

Degree Type

Master of Science


The main purpose of this thesis to examine the controllability and observability of the linear discrete fractional systems. First we introduce the problem and continue with the review of some basic definitions and concepts of fractional calculus which are widely used to develop the theory of this subject. In Chapter 3, we give the unique solution of the fractional difference equation involving the Riemann-Liouville operator of real order between zero and one. Additionally we study the sequential fractional difference equations and describe the way to obtain the state-space repre- sentation of the sequential fractional difference equations. In Chapter 4, we study the controllability and observability of time-invariant linear nabla fractional systems.We investigate the time-variant case in Chapter 5 and we define the state transition matrix in fractional calculus. In the last chapter, the results are summarized and directions for future work are stated.


Discrete Mathematics and Combinatorics | Dynamical Systems | Mathematics | Other Mathematics