On a Caputo-Katugampola fractional differential inclusion

Abstract

We consider a fractional differential inclusion involving Caputo-Katugampola 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
$\lambda $-locally controlable around the null solution for every
$\lambda \in \partial h(z(T))$, where $\partial h$ denotes
Clarke's generalized Jacobian of the locally Lipschitz function
$h$.