Volume 36 • Number 3 • 2013   • Two-Point Boundary Value Problems for Fractional Differential Equations at Resonance Zhigang Hu, Wenbin Liu and Taiyong Chen Abstract. In this paper, by using the coincidence degree theory, we consider the following two-point boundary value problem for fractional differential equation \begin{equation*} \begin{cases} D_{0^+}^{\alpha}x(t)=f(t, x(t), x'(t)), & t\in [0,1], \\ x(0)=0,\ x'(0)=x'(1), & \end{cases} \end{equation*} where $D_{0^+}^\alpha$ denotes the Caputo fractional differential operator of order $ \alpha $, $1< \alpha \leq 2$. A new result on the existence of solutions for above fractional boundary value problem is obtained. 2010 Mathematics Subject Classification: 34A08, 34B15 Full text: PDF