中文摘要：

考虑Banach空间E中分数阶微分方程边值问题{-Dβ0＋u（t）=f（t,u（t））,t∈Ju（0）=u（1）={θ解的存在性,其中1〈β≤2为实数,J=[0,1],Dβ0＋是标准的Riemann-Liouville导数,f：J×E→E连续.用新的非紧性测度估计技巧,在f满足比较一般的增长条件和非紧性测度条件下通过凝聚映射的不动点定理获得了该边值问题解的存在性.

英文摘要：

The existence of solutions for boundary value problems of a nonlinear fractional dilierential equation in a Banach space E was considered, where 1 〈β≤2 was a real number, J = [ O, 1 ] ,D0β. was the standard Riemann-Liouville fractional derivative, and f： J ×E→E was continuous. Since a new estimation technique of noncompactness measure was introduced, under more general conditions of growth and noncompactness measure, the existence of solutions was obtained by using the fixed point theorem of condensing mappings.