Stability of Linear Difference Systems in Discrete and Fractional Calculus

• Main Author: Er, Aynur
• Format: Others
• Published: TopSCHOLAR® 2017
• Subjects: Stability analysis; difference equations; Putzer algorithm; Applied Mathematics; Discrete Mathematics and Combinatorics; Partial Differential Equations
• Online Access: http://digitalcommons.wku.edu/theses/1946; http://digitalcommons.wku.edu/cgi/viewcontent.cgi?article=2950&context=theses

The main purpose of this thesis is to define the stability of a system of linear difference equations of the form, ∇y(t) = Ay(t), and to analyze the stability theory for such a system using the eigenvalues of the corresponding matrix A in nabla discrete calculus and nabla fractional discrete calculus. Discrete exponential functions and the Putzer algorithms are studied to examine the stability theorem. This thesis consists of five chapters and is organized as follows. In the first chapter, the Gamma function and its properties are studied. Additionally, basic definitions, properties and some main theorem of discrete calculus are discussed by using particular example. In the second chapter, we focus on solving the linear difference equations by using the undetermined coefficient method and the variation of constants formula. Moreover, we establish the matrix exponential function which is the solution of the initial value problems (IVP) by the Putzer algorithm.