Journal of Applied Mathematics
Volume 2012 (2012), Article ID 841349, 18 pages
http://dx.doi.org/10.1155/2012/841349
Research Article

The Existence of Solutions for a Fractional 2 𝑚 -Point Boundary Value Problems

Gang Wang,1 Wenbin Liu,1 Jinyun Yang,2 Sinian Zhu,1 and Ting Zheng1

1Department of Mathematics, China University of Mining and Technology, Xuzhou 221008, China
2School of Mathematics and Physical Sciences, Xuzhou Institute of Technology, Xuzhou 221008, China

Received 24 June 2011; Revised 9 October 2011; Accepted 11 October 2011

Academic Editor: Yongkun Li

Copyright © 2012 Gang Wang 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

By using the coincidence degree theory, we consider the following 2 𝑚 -point boundary value problem for fractional differential equation 𝐷 𝛼 0 + 𝑢 ( 𝑡 ) = 𝑓 ( 𝑡 , 𝑢 ( 𝑡 ) , 𝐷 𝛼 − 1 0 + 𝑢 ( 𝑡 ) , 𝐷 𝛼 − 2 0 + 𝑢 ( 𝑡 ) ) + 𝑒 ( 𝑡 ) , 0 < 𝑡 < 1 , 𝐼 3 − 𝛼 0 + 𝑢 ( 𝑡 ) | 𝑡 = 0 = 0 , 𝐷 𝛼 − 2 0 + ∑ 𝑢 ( 1 ) = 𝑚 − 2 𝑖 = 1 𝑎 𝑖 𝐷 𝛼 − 2 0 + 𝑢 ( 𝜉 𝑖 ∑ ) , 𝑢 ( 1 ) = 𝑚 − 2 𝑖 = 1 𝑏 𝑖 𝑢 ( 𝜂 𝑖 ) , where 2 < 𝛼 ≤ 3 , 𝐷 𝛼 0 + and 𝐼 𝛼 0 + are the standard Riemann-Liouville fractional derivative and fractional integral, respectively. A new result on the existence of solutions for above fractional boundary value problem is obtained.