CONVERGENCE ARIES OF A NEW TRIVARIATE MITTAG-LEFFLER-TYPE FUNCTION

Abstract

This article studies the main analytical properties of a new three-variable Mittag-Leffler
type function. The convergence domains of the corresponding triple power series are determined. The
convergence analysis is carried out based on Horn's convergence theory and the asymptotic properties of the
gamma function for large arguments. Twenty-seven different combinations of parameters are considered,
and for each case necessary and sufficient conditions for the absolute convergence of the series are
established, along with some particular cases of ML. The obtained results enrich the theory of fractional
differential equations and provide an effective analytical basis for investigating problems involving the
Prabhakar fractional derivative.