Abstract: We considered the Caputo fractional differential equation with RiemannStieltjes integral boundary condition. We established the existence theorems of positive solutions for the integral boundary value problem of fractional differential equations under the condition of allowing the singularity of the nonlinear term, and proved the existence theorem by using mixed monotone operator method and fixed point theorem on semiordered set. Some examples show the applicability of the conclusion.

Key words: singular, mixed monotone operator, fixed point theorem, positive solution, boundary value problem, RiemannStieltjes integral, Caputo fractional differential equation