Abstract

We consider a class of boundary value problem in a separable Banach space E governed by a fractional differential inclusion with integral boundary conditions w−Dαu(t)∈F(t,u(t),w−Dα−1u(t)),t∈[0,1],Iβu(t)|t=0=0,u(1)=∫20u(t)dt, where α∈]1,2], β∈]0,∞[ are given constants and w−Dγ is the fractional w Riemann-Liouville derivative of order γ∈{α−1,α}, F:[0,1]×E×E↪E is a convex compact valued multimapping. Topological properties of the solutions set are presented. An application to control problems is provided involving Young measure.