Advances in Computational Mathematics

, Volume 39, Issue 1, pp 205–225 | Cite as

Evaluation of generalized Mittag–Leffler functions on the real line

  • Roberto GarrappaEmail author
  • Marina Popolizio


This paper addresses the problem of the numerical computation of generalized Mittag–Leffler functions with two parameters, with applications in fractional calculus. The inversion of their Laplace transform is an effective tool in this direction; however, the choice of the integration contour is crucial. Here parabolic contours are investigated and combined with quadrature rules for the numerical integration. An in-depth error analysis is carried out to select suitable contour’s parameters, depending on the parameters of the Mittag–Leffler function, in order to achieve any fixed accuracy. We present numerical experiments to validate theoretical results and some computational issues are discussed.


Mittag–Leffler function Laplace transform Fractional calculus Contour integral 

Mathematics Subject Classifications (2010)

33E12 44A10 26A33 65D30 


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© Springer Science+Business Media, LLC. 2012

Authors and Affiliations

  1. 1.Dipartimento di MatematicaUniversità degli Studi di Bari “Aldo Moro”BariItaly
  2. 2.Dipartimento di Matematica e Fisica “Ennio De Giorgi”Università del SalentoLecceItaly

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