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

The solution to systems of moment differential equations of the form $z{\mathrm{\partial }}_{m}y=(zA+B)y$ 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.