Fractional functional differential inclusions with finite delay

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, D α y ( t ) ∈ F ( t , y t ) , a.e. t ∈ [ 0 , b ] , 0 < α < 1 , y ( t ) = ϕ ( t ) , t ∈ [ − r , 0 ] , where J = [ 0 , b ] , D α is the standard Riemann–Liouville fractional derivative, and F is a set-valued map.