An Alpha-Beta Phase Diagram Representation of the Zeros and Properties of the Mittag-Leffler Function

Abstract

A significant advance in characterizing the nature of the zeros and organizing the Mittag-Leffler functions into phases according to their behavior is presented. Regions have been identified in the domain of and where the Mittag-Leffler functions , () have not only the same type of zeros but also exhibit similar functional behavior, and this permits the establishment of an - phase diagram.