Table of Contents
ISRN Mathematical Analysis
Volume 2011, Article ID 468346, 14 pages
http://dx.doi.org/10.5402/2011/468346
Research Article

Existence Results for a Coupled System of Nonlinear Fractional Differential Equation with Four-Point Boundary Conditions

1Faculty of Education Al-Arish, Suez Canal University, Ismailia 41522, Egypt
2Faculty of Computers and Informatics, Suez Canal University, Ismailia 41522, Egypt

Received 30 August 2011; Accepted 20 October 2011

Academic Editor: J.-L. Wu

Copyright © 2011 M. Gaber and M. G. Brikaa. 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 coupled system of nonlinear fractional differential equation with four-point boundary conditions. Applying the Schauder fixed-point theorem, an existence result is proved for the following system: 𝐷 𝛼 𝑒 ( 𝑑 ) = 𝑓 ( 𝑑 , 𝑣 ( 𝑑 ) , 𝐷 π‘š 𝑣 ( 𝑑 ) ) , 𝑑 ∈ ( 0 , 1 ) , 𝐷 𝛽 𝑣 ( 𝑑 ) = 𝑓 ( 𝑑 , 𝑒 ( 𝑑 ) , 𝐷 𝑛 𝑒 ( 𝑑 ) ) , 𝑑 ∈ ( 0 , 1 ) , 𝑒 ( 0 ) = 𝛾 𝑒 ( 𝜁 ) , 𝑒 ( 1 ) = 𝛿 𝑒 ( πœ‚ ) , 𝑣 ( 0 ) = 𝛾 𝑣 ( 𝜁 ) , 𝑣 ( 1 ) = 𝛿 𝑣 ( πœ‚ ) , where 𝛼 , 𝛽 , π‘š , 𝑛 , 𝜁 , πœ‚ , 𝛾 , 𝛿 satisfy certain conditions.