%0 Journal Article
%T Three point boundary value problems of fractional functional differential equations with delay
%A Yanan Li
%A Shurong Sun
%A Dianwu Yang and Zhenlai Han
%J Boundary Value Problems
%D 2013
%I 
%R 10.1186/1687-2770-2013-38
%X In this paper, we study three point boundary value problems of the following fractional functional differential equations involving the Caputo fractional derivative: $$ \begin{array}{ll} ^CD^{\alpha}u(t)=f(t,u_{t},^CD^{\beta}{u(t)}),\; 0<t<1, \\ u'(0)=0,\; u'(1)=\lambda u'(\eta), \end{array} $$ where $^CD^{\alpha},^CD^{\beta}$ devote Caputo fractional derivative, $2<\alpha<3$, $0<\beta<1$, $\eta\in(0,1)$, $1<\lambda<\frac{1}{2\eta}$. We use Green function to reformulate boundary value problems into an abstract operator equation. By means of Schauder fixed point theorem and Banach contraction principle, some existence results of solutions are obtained, respectively. As an application, some examples are presented to illustrate the main results.
%U http://www.boundaryvalueproblems.com/content/2013/1/38/abstract