Volume 37 • Number 4 • 2014   • Existence of Solutions for a Coupled System of Fractional Differential Equations Zhigang Hu, Wenbin Liu and Wenjuan Rui Abstract. In this paper, by using the coincidence degree theory, we consider the following Neumann boundary value problem for a coupled system of fractional differential equations \begin{align*} \left\{ \begin{array}{ll} D_{0^+}^{\alpha}u(t)=f(t,v(t),v'(t)), \ \ t\in (0,1), \\ D_{0^+}^{\beta}v(t)=g(t,u(t),u'(t)), \ \ t\in (0,1), \\ u'(0)=u'(1)=0,\ v'(0)=v'(1)=0, \end{array} \right. \end{align*} where $D_{0^+}^\alpha$, $D_{0^+}^\beta$ are the standard Caputo fractional derivative, $ 1< \alpha \leq 2$, $1< \beta \leq 2$. A new result on the existence of solutions for above fractional boundary value problem is obtained. 2010 Mathematics Subject Classification: 34B15 Full text: PDF