Allan C. Peterson
Date of this Version
Kevin Ahrendt. The Existence of Solutions for a Nonlinear, Fractional Self-Adjoint Difference Equation. PhD thesis, University of Nebraska-Lincoln, 2017.
In this work we will explore a fractional self-adjoint difference equation which involves a Caputo fractional difference. In particular, we will develop a Cauchy function for initial value problems and Green's functions for several different types of boundary value problems. We will use the properties of those Green's functions and the Contraction Mapping Theorem to find sufficient conditions for when a nonlinear boundary value problem has a unique solution. We will also investigate the existence of nonnegative solutions for a nonlinear self-adjoint difference that have particular long run behavior.
Adviser: Allan Peterson