Research Article Existence of Solutions for Nonlocal Boundary Value Problems of Higher-Order Nonlinear Fractional Differential Equations

We study some existence results in a Banach space for a nonlocal boundary value problem involving a nonlinear differential equation of fractional order q given by cDqxt ft, xt, 0 < t < 1, q ∈ m − 1,m, m ∈ N, m ≥ 2,x0 0,x′0 0, x′′0 0,..., xm−20 0, x1 αxη. Our results are based on the contraction mapping principle and Krasnoselskii’s fixed point theorem. Copyright q 2009 B. Ahmad and J. J. Nieto. 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. 1