The Existence of Solutions to a Class of Multipoint Boundary Value Problem of Fractional Differential Equation 
Received:November 26, 2011 Revised:October 09, 2012 
Key Words:
fractional differential equation multipoint boundary value problem coincidence degree.

Fund Project:Supported by the National Natural Science Foundation of China (Grant No.11071001), the Natural Science Foundation of Anhui Province (Grant No.\,1208085MA13) and 211 Project of Anhui University (Grant No.KJTD002B). 

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Abstract: 
In this paper, we consider the following multipoint boundary value problem of fractional differential equation $$\align &D^{\alpha}_{0+}u(t) = f(t, u(t),~D^{\alpha1}_{0+}u(t), D^{\alpha2}_{0+}u(t), D^{\alpha3}_{0+}u(t)),~~t\in(0,1), \\&I^{4\alpha}_{0+}u(0) = 0, ~D^{\alpha1}_{0+}u(0)=\displaystyle{\sum_{i=1}^{m}}\alpha_{i}D^{\alpha1}_{0+}u(\xi_{i}),\\&D^{\alpha2}_{0+}u(1)=\sum\limits_ {j=1}^{n}\beta_{j} D^{\alpha2}_{0+}u(\eta_{j}),~D^{\alpha3}_{0+}u(1)D^{\alpha3}_{0+}u(0)=D^{\alpha2}_{0+}u(\frac{1}{2}),\endalign$$ where $3<\alpha \leq 4$ is a real number. By applying Mawhin coincidence degree theory and constructing suitable operators, some existence results of solutions can be established. 
Citation: 
DOI:10.3770/j.issn:20952651.2013.02.005 
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