Analytical Solutions and Stability Analysis of Linear Multi-Delayed Fractional Systems

In this paper, a class of multi-delayed Mittag--Leffler (ML) type matrix functions is developed, and the Laplace transform is employed to derive explicit analytical representations of the solutions to the corresponding initial value problems (IVPs) for Hilfer fractional linear systems with several delays and nonpermutable coefficient matrices. In addition, the Ulam--Hyers (UH) stability of the proposed fractional multi-delayed model is established. Several nontrivial numerical examples are presented to illustrate the theoretical findings.