Multi-delayed perturbation of Mittag-Leffler 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<α≤l. Our results are new even for the case 1<α<2 and for the classical (α=2) second order single delay and multi-delay linear (fractional) differential equations.