Local Controllability of a Class of Fractional Differential Inclusions via Derived Cones

Abstract

We study a class of fractional differential inclusions defined by Caputo-Katugampola fractional derivative and we provide a sufficient condition for local controllability along a reference trajectory. This condition is obtain in terms of a certain variational fractional differential inclusion associated to the problem studied. More exactly, we prove that the reachable set of a certain variational fractional differential inclusion of Caputo-Katugampola type is a derived cone in the sense of Hestenes to the reachable set of the problem and then, in order to obtain our main result, we essentially use an outstanding property of derived cones and a continuous version of Filippov’s theorem for solutions of the fractional differential inclusion considered.