Abstract: We considered a class of boundary value problems for fractional differential equations with Ψ-Caputo fractional derivative, the boundary conditions included a Stieltjes integral and multiple Ψ-Riemann-Liouville fractional integral operators. Firstly, the expression of solution of corresponding auxiliary boundary value problem was given. Secondly, the existence and uniqueness of solution of the boundary value problem were proved by using Banach compression mapping principle and Schaefer fixed point theorem. Finally, we gave an example to illustrate the validity of the obtained results.

Key words: ψ-Caputo , derivative, Stieltjes integral, multipoint, fixed point theorem