Fast evaluation of the Mittag-Leffler function on the imaginary axis

The Mittag-Leffler function plays a central role in fractional calculus; however its numerical evaluation still remains an expensive and challenging task. In this work we discuss the evaluation of this function for pure imaginary arguments by means of a numerical method performing the inversion of its Laplace transform on a suitably selected integral contour. By means of some numerical experiments we show that the proposed algorithm behaves in an efficient and fast way.