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

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

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.