On the computation of the multidimensional Mittag-Leffler function

Manuel D. Ortigueira, António Mendes Lopes, J. A.Tenreiro Machado

Research output: Contribution to journalArticlepeer-review

5 Citations (Scopus)


The multidimensional Mittag-Leffler function (M-MLF) is an important tool for studying state-space fractional-order linear systems. However, using the M-MLF entails the need of efficient numerical implementations. In this paper we propose two methods for computing the M-MLF. The first is based on an integral formulation. The second adopts the fast Fourier transform. Numerical simulations compare both methods and show their effectiveness. The new algorithms allow a straightforward use of the M-MLF.

Original languageEnglish
Pages (from-to)278-287
Number of pages10
JournalCommunications In Nonlinear Science And Numerical Simulation
Publication statusPublished - 1 Dec 2017


  • Fast Fourier transform
  • Integral formulation
  • Multidimensional Mittag-Leffler function
  • Numerical computation


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