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On the Numerical Computation of the Mittag–Leffler Function

  • Manuel D. Ortigueira , António M. Lopes ORCID logo EMAIL logo and José Tenreiro Machado
Published/Copyright: July 12, 2019

Abstract

The Mittag–Leffler function (MLF) plays an important role in many applications of fractional calculus, establishing a connection between exponential and power law behaviors that characterize integer and fractional order phenomena, respectively. Nevertheless, the numerical computation of the MLF poses problems both of accuracy and convergence. In this paper, we study the calculation of the 2-parameter MLF by using polynomial computation and integral formulas. For the particular cases having Laplace transform (LT) the method relies on the inversion of the LT using the fast Fourier transform. Experiments with two other available methods compare also the computational time and accuracy. The 3-parameter MLF and its calculation are also considered.

Acknowledgements

This work was funded by Portuguese National Funds through the FCT - Foundation for Science and Technology under the project PEst-UID/EEA/00066/2013.

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Received: 2018-11-22
Accepted: 2019-06-07
Published Online: 2019-07-12
Published in Print: 2019-10-25

© 2019 Walter de Gruyter GmbH, Berlin/Boston

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