On a fractional differential inclusion with integral boundary conditions in Banach space

We consider a class of boundary value problem in a separable Banach space E, involving a nonlinear differential inclusion of fractional order with integral boundary conditions, of the form {D(alpha)u(t) is an element of F(t, u(t), D(alpha-1)u(t)), a.e., t is an element of [0, 1], I(beta)u(t) vertical bar(t-0) = 0, u(1) = integral(1)(0) u(t) dt, (*) where D (alpha) is the standard Riemann-Liouville fractional derivative, F is a closed valued mapping. Under suitable conditions we prove that the solutions set of (*) is nonempty and is a retract in W-E(alpha,1) (I). An application in control theory is also provided by using the Young measures.