Some new existence results for fractional differential inclusions with boundary conditions

Abstract

This paper is mainly concerned with the existence of solutions for a certain class of fractional differential inclusions with boundary conditions. By using Bohnenblust–Karlin’s fixed point theorem, a main existence theorem is obtained. As an application of this main theorem, we establish two existence results when the multi-valued nonlinearity F has sub-linear or linear growth in the state variable y . Our results are even new when applied to a corresponding single-valued problem.