Relative controllability of fractional delay differential equations via delayed perturbation of Mittag-Leffler functions

This paper is concerned with the relative controllability of fractional delay systems in control for finite dimensional spaces. A notion of fractional delay Grammian matrix involving two parameter Mittag-Leffler type delay matrix function is introduced. Sufficient and necessary condition is established to examine that linear system is relatively controllable. Controllability result for semilinear system is obtained by Krasnoselskii's fixed point theorem. Examples are given to illustrate theoretically results. (C) 2020 Elsevier B.V. All rights reserved.