On the Matrix Mittag–Leffler Function: Theoretical Properties and Numerical Computation

Abstract

Many situations, as for example within the context of Fractional Calculus theory, require computing the Mittag−Leffler (ML) function with matrix arguments. In this paper, we collect theoretical properties of the matrix ML function. Moreover, we describe the available numerical methods aimed at this purpose by stressing advantages and weaknesses.

Keywords

• mittag–leffler function
• matrix function
• schur decomposition
• laplace transform
• fractional calculus