Multi-delayed perturbation of Mittag-Leftier type matrix functions

Abstract

In this paper, we introduce a multivariate determining function and propose a multi-delayed perturbation of Mittag-Leffler type matrix function. It is an extension of the classical Mittag-Leffler type matrix function and delayed Mittag-Leffler type matrix function. With the help of the multi-delayed perturbation of Mittag-Leffler type matrix function, we give an explicit analytical solution to linear nonhomogeneous Riemann-Liouville fractional multi-delay differential equations of order l-1 < alpha <= l. Our results are new even for the case 1 < alpha < 2 and for the classical (alpha = 2) second order single delay and multi-delay linear (fractional) differential equations. (c) 2021 Elsevier Inc. All rights reserved.