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Journal of Applied Mathematics
Volume 2011, Article ID 298628, 51 pages
http://dx.doi.org/10.1155/2011/298628
Review Article

Mittag-Leffler Functions and Their Applications

1Office for Outer Space Affairs, United Nations, Vienna International Centre, P.O. Box 500, 1400 Vienna, Austria
2Department of Mathematics and Statistics, McGill University, Montreal, QC, Canada H3A 2K6
3Centre for Mathematical Sciences, Pala Campus, Arunapuram P.O., Pala, Kerala 686574, India
4Department of Mathematics and Statistics, Jai Narain Vyas University, Jodhpur 342005, India

Received 15 December 2010; Accepted 28 February 2011

Academic Editor: Ch Tsitouras

Copyright © 2011 H. J. Haubold 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.

Abstract

Motivated essentially by the success of the applications of the Mittag-Leffler functions in many areas of science and engineering, the authors present, in a unified manner, a detailed account or rather a brief survey of the Mittag-Leffler function, generalized Mittag-Leffler functions, Mittag-Leffler type functions, and their interesting and useful properties. Applications of G. M. Mittag-Leffler functions in certain areas of physical and applied sciences are also demonstrated. During the last two decades this function has come into prominence after about nine decades of its discovery by a Swedish Mathematician Mittag-Leffler, due to the vast potential of its applications in solving the problems of physical, biological, engineering, and earth sciences, and so forth. In this survey paper, nearly all types of Mittag-Leffler type functions existing in the literature are presented. An attempt is made to present nearly an exhaustive list of references concerning the Mittag-Leffler functions to make the reader familiar with the present trend of research in Mittag-Leffler type functions and their applications.