Dassios, Ioannis K.Ioannis K.DassiosTzounas, GeorgiosGeorgiosTzounasMilano, FedericoFedericoMilano2024-04-252024-04-252019 Elsev2019-11-15Applied Mathematics and Computation0096-3003http://hdl.handle.net/10197/25765The main objective of this article is to provide a link between the solutions of an initial value problem of a linear singular system of differential equations and the solutions of its proper M-systems, i.e., systems that appear after applying the generalized Möbius transform to the pencil of the original singular system (prime system). Firstly, we prove that by using the pencil of the prime system we can study the existence and uniqueness of solutions of its proper M-systems. Moreover these solutions can be explicitly represented without resorting to any further processes of computations. Finally, numerical examples are given to illustrate our theory.enThis is the author’s version of a work that was accepted for publication in Applied Mathematics and Computation. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Applied Mathematics and Computation (VOL 361, (15 November 2019)) DOI: https://doi.org/10.1016/j.amc.2019.05.047SingularityDynamical systemMöbius transformInitial conditionsDifferential equationsJournal Article36133835310.1016/j.amc.2019.05.0472023-09-2015/IA/3074https://creativecommons.org/licenses/by-nc-nd/3.0/ie/