General Delayed Perturbation of the Three-Parameter Mittag-Leffler Functions

Abstract

In this paper, we define a general delayed perturbation of the three-parameter Mittag-Leffler type matrix function, which can be seen as a generalization of both the delayed perturbation of the two-parameter Mittag-Leffler type function and the delayed perturbation of the three-parameter Mittag-Leffler type function. We examine a couple of its properties in addition to identifying some of its relations with the existing Mittag-Leffler-type functions in the literature. We present an explicit formula by constructing on the general delayed perturbation of the three-parameter Mittag-Leffler type function as a solution to a linear fractional differential delayed equation with two distinct approaches.