Special Session 23: Topological and Variational Methods for Differential Equations

Comparison of Green`s Functions for Two-Point Boundary Value Problems with Fractional Derivative Boundary Conditions

Paul Eloe
Univeristy of Dayton
USA
Co-Author(s):    Jeffrey T. Neugebauer
Abstract:
In this paper, we compare Green`s functions for two point fractional differential equations where both conditions at the right endpoint depend on a fractional derivative. This is accomplished by showing that the difference of two Green`s functions is sufficiently smooth and satisfies a fractional boundary value problem. The sign of the solution of this boundary value problem depends on a fractional derivative of a Green`s function evaluated at the right endpoint. These results answer an open question raised by the authors in a previous paper.