The Mittag-Leffler (ML) function plays a fundamental role in fractional
calculus but very few methods are available for its numerical evaluation. In
this work we present a method for the efficient computation of the ML function
based on the numerical inversion of its Laplace transform (LT): an optimal
parabolic contour is selected on the basis of the distance and the strength of
the singularities of the LT, with the aim of minimizing the computational
effort and reduce the propagation of errors. Numerical experiments are
presented to show accuracy and efficiency of the proposed approach. The
application to the three parameter ML (also known as Prabhakar) function is
also presented.Comment: Accepted for publication in SIAM Journal on Numerical Analysi
