On the computation of the multidimensional Mittag-Leffler function

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.