, Volume 38, Issue 1-2, pp 225-241
Date: 16 Feb 2011

Existence and uniqueness of positive solutions to m-point boundary value problem for nonlinear fractional differential equation

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Abstract

In this paper, we consider the following nonlinear fractional m-point boundary value problem where \(D_{0+}^{\alpha}\) is the standard Riemann-Liouville fractional derivative. By the properties of the Green function, the lower and upper solution method and fixed-point theorem in partially ordered sets, some new existence and uniqueness of positive solutions to the above boundary value problem are established. As applications, examples are presented to illustrate the main results.