关键词: 分数阶微分方程, 积分边值问题, 不动点指数, 正解, 存在性

Abstract: By using the theory of fixed-point index, we considered a class of  integral boundary value problems of fractional differential equations under the conditions related to the first eigenvalue of the corresponding linear operator. We obtained the result that there
 was at least one positive solution for the integral boundary value problem, and gave an example to illustrate the applicability of the theorem.

Key words: fractional differential equation, integral boundary value problem, fixed-point index, positive solution, existence