MULTIVARIATE MITTAG-LEFFLER FUNCTION

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.