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

Abstract

We investigate an m-point boundary value problem for nonlinear fractional differential equations. The associated Green function for the boundary value problem is given at first, and some useful properties of the Green function are obtained. By using the fixed point theorems of cone expansion and compression of norm type and Leggett-Williams fixed point theorem, the existence of multiple positive solutions is obtained. © 2011 Moustafa El-Shahed and Wafa M. Shammakh.