Abstract：Differential equations with fractional order have proved to be extensive application in engineering problems, including new material science, fluid mechanics, viscoelasticity mechanics, electronic circuit, analytical chemistry and so on. Furthermore, biology, economics, optimal control and some practical problems can be solved by establishing differential inclusion models for theoretical analysis and research. In recent years, the studies on fractional differential equations and fractional differential inclusions with boundary value problems have got much attention. Based on the study of the existence of solutions for a class of fractional differential equations proposed by CABADA and WANG, we extend their results to cover the multivalued case. In this paper, based on the fixedpoint theorem for multivalue maps, we have studied the following fractional order differential inclusions with integral boundary value problems:CD0+αy(t)∈F(t,y(t)), t∈(0,1), α∈(2,3), y(0)=y''(0)=0, y(1)=λ∫10y(s)ds. The sufficient conditions for the existence of solutions to the fractional order differential inclusions with integral boundary value conditions are established. Our results include the cases when the nonlinearity is convex as well as nonconvex valued.