Abstract and Applied Analysis
Volume 2009 (2009), Article ID 494720, 9 pages
doi:10.1155/2009/494720
Research Article

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

Bashir Ahmad1 and Juan J. Nieto2

1Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia
2Departamento de Análisis Matemático, Facultad de Matemáticas, Universidad de Santiago de Compostela, 15782 Santiago de Compostela, Spain

Received 19 February 2009; Accepted 27 April 2009

Academic Editor: Paul Eloe

Copyright © 2009 Bashir Ahmad and Juan 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.

Abstract

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 cDqx(t)=f(t,x(t)), 0<t<1, q∈(m−1,m], m∈ℕ, m≥2, x(0)=0, x′(0)=0, x′′(0)=0,…,x(m−2)(0)=0, x(1)=αx(η). Our results are based on the contraction mapping principle and Krasnoselskii's fixed point theorem.