Existence and uniqueness of positive solutions for integral boundary value problems of fractional differential equations

Abstract This paper investigates a class of singular nonlinear fractional differential equations with Riemann-Stieltjes integral boundary conditions. The equation contains Riemann-Liouville fractional derivatives, and the nonlinear term depends on both the unknown function and its fractional derivative. By constructing an appropriate cone and employing the cone expansion and compression fixed point theorem, the existence of positive solutions is proved. The uniqueness of positive solutions is established using the Banach contraction mapping principle, and the local Ulam-Hyers stability of the equation is also proved for sufficiently small perturbations. The results obtained in this paper generalize related conclusions in the existing literature.