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The Existence of Solutions for a Nonlinear, Fractional Self-Adjoint Difference Equation
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.
Ahrendt, Kevin, "The Existence of Solutions for a Nonlinear, Fractional Self-Adjoint Difference Equation" (2017). ETD collection for University of Nebraska - Lincoln. AAI10271807.