On the Numerical Computation of the Mittag-Leffler Function

Manuel D. Ortigueira, António M. Lopes, José Tenreiro Machado

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)
76 Downloads (Pure)


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.

Original languageEnglish
Pages (from-to)725-736
JournalInternational Journal of Nonlinear Sciences and Numerical Simulation
Issue number6
Publication statusPublished - Oct 2019


  • fast Fourier transform
  • Mittag-Leffler function
  • numerical computation


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