On a study for the neutral Caputo fractional multi-delayed differential equations with noncommutative coefficient matrices

Abstract

The representation of a solution to a neutral linear fractional multiple-delay differential inhomogeneous system with non-commutative coefficient matrices is studied using a multiple-delay perturbation of a matrix function of the Mittag-Leffler type. Second, the existence and uniqueness of the solution are discussed along with the Ulam-Hyers stability of a semilinear neutral fractional differential with multiple delays. Thirdly, with the help of the Krasnoselskii's fixed point theorem, a sufficient condition for the relative controllability of a semilinear neutral fractional differential system with multiple-delay is obtained. Numerical examples confirm the theoretical conclusions. (C) 2022 Elsevier Ltd.