  In this paper, we propose a delayed perturbation of Mittag-Leffler type
matrix function, which is an extension of the classical Mittag-Leffler type
matrix function and delayed Mittag-Leffler type matrix function. With the help
of the delayed perturbation of Mittag-Leffler type matrix function, we give an
explicit formula of solutions to linear nonhomogeneous fractional delay
differential equations.
