On nonlinear neutral Liouville–Caputo-type fractional differential equations with Riemann–Liouville integral boundary conditions

Abstract

AbstractThis paper studies neutral Liouville–Caputo-type fractional differential equations and inclusions supplemented with nonlocal Riemann–Liouville-type integral boundary conditions. Sadovskii’s fixed point theorem is applied to establish the existence result for the single-valued case, while the multivalued case is investigated by using nonlinear alternative for contractive maps. Examples are constructed to illustrate the main results. The case of nonlinear nonlocal boundary conditions is also discussed.