Fractional differential inclusions with anti-periodic boundary conditions in Banach spaces.

The main purpose of this paper is to provide the theory of differential inclu- sions by new existence results of solutions for boundary value problems of differential inclusions with fractional order and with anti-periodic boundary conditions in Banach spaces. We prove existence theorems of solutions under both convexity and nonconvex- ity conditions on the multivalued side. Meanwhile, the compactness of the set solutions is also established.