Copyright © 2013 Shang-lin Yao et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We investigate the existence of multiple positive solutions for three-point boundary value problem of fractional differential equation with -Laplacian operator , where are the standard Riemann-Liouville derivatives with , and the constant is a positive number satisfying ; -Laplacian operator is defined as . By applying monotone iterative technique, some sufficient conditions for the existence of multiple positive solutions are established; moreover iterative schemes for approximating these solutions are also obtained, which start off a known simple linear function. In the end, an example is worked out to illustrate our main results.