Mathematical Problems in Engineering
Volume 2009 (2009), Article ID 535209, 17 pages
doi:10.1155/2009/535209
Research Article

Singular Positone and Semipositone Boundary Value Problems of Nonlinear Fractional Differential Equations

Chengjun Yuan,1,2 Daqing Jiang,1 and Xiaojie Xu1

1School of Mathematics and Statistics, Northeast Normal University, Changchun 130024, Jilin, China
2School of Mathematics and Computer, Harbin University, Harbin 150086, Heilongjiang, China

Received 8 January 2009; Accepted 15 April 2009

Academic Editor: Victoria Vampa

Copyright © 2009 Chengjun Yuan 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

We present some new existence results for singular positone and semipositone nonlinear fractional boundary value problem D0+αu(t)=μa(t)f(t,u(t)),  0<t<1, u(0)=u(1)=u′(0)=u′(1)=0, where μ>0, a, and f are continuous, α∈(3,4] is a real number, and D0+α is Riemann-Liouville fractional derivative. Throughout our nonlinearity may be singular in its dependent variable. Two examples are also given to illustrate the main results.