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Abstract: 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, where is the standard Riemann–Liouville fractional derivative, and is a set-valued map. [Copyright &y& Elsevier]

Abstract: In this paper, we study fractional differential inclusions with Dirichlet boundary conditions. We prove the existence of a solution under both convexity and nonconvexity conditions on the multi-valued right-hand side. The proofs rely on nonlinear alternative Leray–Schauder type, Bressan–Colombo selection theorem and Covitz and Nadler’s fixed point theorem for multi-valued contractions. The compactness of the set solutions and relaxation results is also established. In the last section we consider the fractional boundary value problem with infinite delay. [Copyright &y& Elsevier]