Fractional functional differential inclusions with finite delay

In this paper, we present fractional versions of the Filippov theorem and the Filippov-Wazewski theorem, as well as an existence result, compactness of the solution set and Hausdorff continuity of operator solutions for functional differential inclusions with fractional order, Dα y (t) ∈ F (t, yt), a.e. t ∈ [0, b], 0 < α < 1,y (t) = φ{symbol} (t), t ∈ [- r, 0], where J = [0, b], Dα is the standard Riemann-Liouville fractional derivative, and F is a set-valued map. © 2008 Elsevier Ltd. All rights reserved.