关键词: Banach压缩映像原理, 正解, 分数阶微分方程, 分布时滞, Liouville导数

Abstract: The existence of a positive solution of the fractional differential equations with distributed delays was studied using the Banach contraction principle and some necessary analytic techniques. A sufficient condition for a positive solution of the equations was obtained. An example was provided to illustrate the effectiveness of the theorem.

Key words: Banach contraction principle, positive solution, fractional differential equations, distributed delays, Liouville derivative