Some boundary value problems of fractional differential equations and inclusions

In this paper, we study the existence of solutions for nonlinear fractional differential equations and inclusions of order q∈(1,2]q∈(1,2] with families of mixed and closed boundary conditions. In case of inclusion problems, the existence results are established for convex as well as nonconvex multivalued maps. Our results are based on Leray–Schauder degree theory, nonlinear alternative of Leray–Schauder type, and some fixed point theorems for multivalued maps. Some interesting special cases are also discussed.