中文摘要：

应用拉伸压缩不动点定理研究非线性分数阶微分方程特征值问题的正解,得到了正解的存在性.结果表明,对于一类α阶非线性分数阶微分方程的特征值问题（3〈α≤4）,当特征值参数满足在一给定开区间时,该微分方程至少存在一个正解.

英文摘要：

We used the fixed point theorem of cone expansion and cone compression to study the eigenvalue problem of nonlinear fractional differential equation so as to obtain the existence of positive solutions.The results show that for a type ofα-order fractional differential equation eigenvalue problem（3〈α≤4）,the differential equation has at least one positive solution when eigenvalue parameter belongs to an open interval.