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Advances in Mathematical Physics
Volume 2013 (2013), Article ID 421685, 13 pages
Research Article

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

Department of Physics, University of Memphis, Memphis, TN 38152, USA

Received 8 May 2013; Accepted 25 June 2013

Academic Editor: Dumitru Baleanu

Copyright © 2013 John W. Hanneken et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.