Mittag-Leffler Functions and Their Applications

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 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 G.M. Mittag-Leffler, due its vast potential of its applications in solving the problems of physical, biological, engineering and earth sciences etc. 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.