Delayed perturbation of Mittag-Leffler functions and their applications to fractional linear delay differential equations

TL;DR

This paper introduces a delayed perturbation of Mittag-Leffler matrix functions, extending classical functions, and provides explicit solutions for linear nonhomogeneous fractional delay differential equations.

Contribution

It presents a novel delayed perturbation of Mittag-Leffler functions and derives explicit solutions for fractional delay differential equations.

Findings

Extended Mittag-Leffler functions to include delays

Explicit solution formulas for fractional delay differential equations

Enhanced mathematical tools for fractional calculus applications

Abstract

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.