Positive solutions of the three-point boundary value problem for fractional-order differential equations with an advanced argument

Abstract

In this article, we consider the existence of at least one positive solution to the three-point boundary value problem for nonlinear fractional-order differential equation with an advanced argument (Equation presented) where 2 < a ≤ 3, 0 < 1, 0 < β < 1/η, CD α is the Caputo fractional derivative. Using the well-known Guo-Krasnoselskii fixed point theorem, sufficient conditions for the existence of at least one positive solution are established. © 2011 Wang et al; licensee Springer.