On linear systems of moment differential equations with singularities of the first kind

TL;DR

This paper develops solutions for systems of moment differential equations with singularities, introducing a generalized matrix power and analyzing Floquet-type solutions, with applications demonstrated through examples.

Contribution

It provides a new approach to solving moment differential systems with singularities, including a generalized matrix power and Floquet solution analysis.

Findings

Existence of Floquet-type solutions established.

A generalized definition of $z^B$ introduced.

Applications demonstrated with relevant examples.

Abstract

The solution to systems of moment differential equations of the form $z\partial_my=(zA+B)y$ are provided, for a matrix $B$ with general good spectrum. Existence and convergence of Floquet-type solutions is studied. A generalized definition of $z^B$ is given, as a tool to solve the main problem whenever $A\equiv 0$. The theory is illustrated with examples which are important in applications.