We consider the following fractional differential inclusionformulawhere F(:; :) : [0; T] £ R ! P(R) is a set-valued map, D¾C F denotes CaputoFabrizio’s fractional derivative of order ¾ 2 (1; 2) and X0;X1 ½ R are closed sets. We prove that the reachable set of a certain variational fractional differential inclusion is a derived cone in the sense of Hestenes to the reachable set of the problem (1). In order to obtain the continuity property in the definition of a derived cone we shall use a continuous version of Filippov’s theorem for solutions of fractional differential inclusions (1). As an application we obtain a sufficient condition for local controllability along a reference trajectory