Abstract
In this paper, we study a new class of single-valued and multi-valued boundary value problems involving multiple fractional derivatives of the Caputo type and the Riemann-Liouville type fractional integral boundary conditions. The existence results for the single valued case are based on the contraction mapping principle, nonlinear alternative of the Leray-Schauder type and the Krasnoselski's fixed point theorem, while the results for the multivalued case are obtained by applying the Leray-Schauder nonlinear alternative and the Covitz-Nadler fixed point theorem. Examples illustrating the main results are also presented. Some generalizations involving the Riemann-Liouville type integral and discrete multipoint boundary conditions are also addressed.