Abstract:
This thesis presents an exploration of a variant of the multivariate Mittag-Leffler
function, with a focus on its properties and applications in the context of solving
differential equations. The work includes several theorems related to the convergence,
Laplace transform, and integral representation of the function, as well as an analysis
of its usefulness as a tool for constructing solutions to certain classes of fractional
differential equations with constant coefficients. Notably, the methods discussed are
not limited to fractional derivative operators, but can also be applied to high-order
ordinary differential equations.