Aurelian Cernea†
Abstract: We consider a fractional differential inclusion involving CaputoFabrizio 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 hlocally 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.
MSC: 34A60, 26A33, 26A42, 34B15.
keywords: fractional derivative, differential inclusion, local controllability
DOI 10.56082/annalsarscimath.2020.1-2.51
† acernea@fmi.unibuc.ro Faculty of Mathematics and Computer Science, University of Bucharest, Academiei 14, 010014 Bucharest and Academy of Romanian Scientists, Splaiul Independen¸tei 54, 050094 Bucharest, Romania
PUBLISHED in Annals Academy of Romanian Scientists Series on Mathematics and Its Application, Volume 12 no 1-2, 2020
