Title: Solutions to a discrete, nonlinear, (N­1,1) fractional boundary value problem

Authors: Michael Holm

Addresses: The University of Nebraska–Lincoln, USA

Abstract: We consider a discrete, nonlinear, (N ­1, 1) fractional-order boundary value problem in one variable with a fractional-order derivative specified as the right boundary condition. We first derive and establish properties of the corresponding Green|s function and then apply these properties – together with Krasnosel|skii|s Theorem and Banach|s Contraction Mapping Theorem – to show the existence of a positive solution to the given problem.

Keywords: dynamical systems; discrete fractional calculus; two-point boundary value problem; Green|s function; Krasnosel|skii theorem; Banach; contraction mapping theorem; nonlinear boundary value problems.

DOI: 10.1504/IJDSDE.2011.038506

International Journal of Dynamical Systems and Differential Equations, 2011 Vol.3 No.1/2, pp.267 - 287

Published online: 09 Feb 2011 *

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