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      Mittag-Leffler Functions and Their Applications

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      Journal of Applied Mathematics

      Hindawi Limited

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          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.

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          Most cited references 39

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          The random walk's guide to anomalous diffusion: a fractional dynamics approach

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            On the Appearance of the Fractional Derivative in the Behavior of Real Materials

             P. Torvik,  R. Bagley (1984)
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              On Mittag-Leffler-type functions in fractional evolution processes

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                Author and article information

                Journal
                Journal of Applied Mathematics
                Journal of Applied Mathematics
                Hindawi Limited
                1110-757X
                1687-0042
                2011
                2011
                : 2011
                :
                : 1-51
                10.1155/2011/298628
                © 2011

                http://creativecommons.org/licenses/by/3.0/

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