中文摘要：

本文研究非线性分数阶积分边值问题D0＋ a u（t）=f9t,u（t））, 1〈a≤2,t∈[0,T]，T〉0, I 0＋ 2-a u（t）｜t=0=0, D0＋ a-2 u（T）=∑i=1 m ai I0＋ a-2 u（ξi）解的存在性，其中D0＋ a, I0＋ a分别是标准的Riemann—Liouville型分数阶导数和积分，利用不动点定理得到该边值问题解的存在性和唯一性结果，并举例验证了结果的合理性．

英文摘要：

In this paper, we study the existence of solutions of the following nonlinear fractional integro-differential equations boundary value problem D0＋ a u（t）=f9t,u（t））, 1〈a≤2,t∈[0,T],T〉0, I 0＋ 2-a u（t）｜t=0=0, D0＋ a-2 u（T）=∑i=1 m ai I0＋ a-2 u（ξi）,where D0＋ a and I0＋ a are the standard Riemann-Liouville fractional derivative and fractional integral respectively. Some existence and uniqueness results are obtained by applying some standard fixed point principles. Several examples are given to illustrate the results.