The $\mu$-neutral fractional multi-delayed differential equations

TL;DR

This paper introduces a new class of $$-neutral fractional multi-delayed differential systems with noncommutative matrices, proposing a novel Mittag-Leffler type matrix function and analyzing solution existence, uniqueness, and stability.

Contribution

It presents the first explicit solution method for $$-neutral systems with noncommutative matrices and establishes conditions for solution existence, uniqueness, and stability.

Findings

Explicit solution derived for the system

Proved existence and uniqueness of solutions

Discussed stability using fixed point theory

Abstract

The $\mu$-neutral linear fractional multi-delayed differential nonhomogeneous system with noncommutative coefficient matrices is introduced. The novel $\mu$-neutral multi-delayed perturbation of Mittag-Leffler type matrix function is proposed. Based on this, an explicit solution to the system is investigated step by step. The existence uniqueness of solutions to $\mu$-neutral nonlinear fractional multi-delayed differential system is obtained with regard to the supremum norm. The notion of stability analysis in the sense of solutions to the described system is discussed on the grounds of the fixed point approach.