Eur. Phys. J. Special Topics 226, 3591–3607 (2017)
https://doi.org/10.1140/epjst/e2018-00076-4

Regular Article

Impulsive control functional differential systems of fractional order: stability with respect to manifolds

¹ Missouri S&T, Department of Mathematics and Statistics, Rolla, MO 65409-0020, USA
² University of Texas at San Antonio, Department of Mathematics, San Antonio, TX 78249, USA
³ Technical University, Department of Mathematics and Physics, 8800 Sliven, Bulgaria

^a e-mail: ivanka.stamova@utsa.edu

Received: 18 August 2017
Received in final form: 3 December 2017
Published online: 25 July 2018

Abstract

In this paper, we consider nonlinear impulsive functional differential systems involving Caputo fractional derivatives. Using vector multivariable piecewise continuous Lyapunov functions and a new vector fractional comparison principle, stability criteria with respect to a manifold are established. Some examples are presented in order to illustrate our theoretical findings.