On controllability for fractional differential inclusion

We consider a fractional differential inclusion involving Caputo´s fractional derivative and we obtain a sufficient condition for h-local controllability along a reference trajectory. To derive this result we use convex linearizations of the fractional differential inclusion. More precisely, we show that the fractional differential inclusion is h-locally controlable around a solution z if a certain linearized inclusion is λ-locally controlable around the null solution for every λ ∈ ∂h(z(T)), where ∂h denotes Clarke´s generalized Jacobian of the locally Lipschitz function h.