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The European Physical Journal Special Topics

, Volume 226, Issue 16–18, pp 3427–3443 | Cite as

Comments on the properties of Mittag-Leffler function

  • G. Dattoli
  • K. Gorska
  • A. Horzela
  • S. Licciardi
  • R. M. Pidatella
Regular Article
  • 9 Downloads
Part of the following topical collections:
  1. Fractional Dynamical Systems - Recent Trends in Theory and Applications

Abstract

The properties of Mittag-Leffler function are reviewed within the framework of an umbral formalism. We take advantage from the formal equivalence with the exponential function to define the relevant semigroup properties. We analyse the relevant role in the solution of Schrödinger type and heat-type fractional partial differential equations and explore the problem of operatorial ordering finding appropriate rules when non-commuting operators are involved. We discuss the coherent states associated with the fractional Schödinger equation, analyze the relevant Poisson type probability amplitude and compare with analogous results already obtained in the literature.

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Copyright information

© EDP Sciences and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.ENEA – Frascati Research CenterFrascati, RomeItaly
  2. 2.H.Niewodniczanski Institute of Nuclear Physics, Polish Academy of SciencesKrakowPoland
  3. 3.Dep. of Mathematics and Computer Science, University of CataniaCataniaItaly

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