Advances in Difference Equations
Volume 2011 (2011), Article ID 107384, 11 pages
doi:10.1155/2011/107384
Research Article

New Existence Results for Nonlinear Fractional Differential Equations with Three-Point Integral Boundary Conditions

Bashir Ahmad,1 Sotiris K. Ntouyas,2 and Ahmed Alsaedi1

1Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia
2Department of Mathematics, University of Ioannina, 451 10 Ioannina, Greece

Received 30 October 2010; Revised 12 December 2010; Accepted 12 December 2010

Academic Editor: Dumitru Baleanu

Copyright © 2011 Bashir Ahmad 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

This paper studies a boundary value problem of nonlinear fractional differential equations of order 𝑞 ∈ ( 1 , 2 ] with three-point integral boundary conditions. Some new existence and uniqueness results are obtained by using standard fixed point theorems and Leray-Schauder degree theory. Our results are new in the sense that the nonlocal parameter in three-point integral boundary conditions appears in the integral part of the conditions in contrast to the available literature on three-point boundary value problems which deals with the three-point boundary conditions restrictions on the solution or gradient of the solution of the problem. Some illustrative examples are also discussed.