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Open AccessArticle

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

1
Department of Electrical and Information Engineering, Polytechnic University of Bari, Via E. Orabona n.4, 70125 Bari, Italy
2
INdAM Research Group GNCS, Istituto Nazionale di Alta Matematica “Francesco Severi”, Piazzale Aldo Moro 5, 00185 Rome, Italy
Mathematics 2019, 7(12), 1140; https://doi.org/10.3390/math7121140
Received: 14 October 2019 / Revised: 16 November 2019 / Accepted: 18 November 2019 / Published: 21 November 2019
(This article belongs to the Special Issue Advanced Mathematical Methods: Theory and Applications)
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. View Full-Text
Keywords: Mittag–Leffler function; matrix function; Schur decomposition; Laplace transform; fractional calculus Mittag–Leffler function; matrix function; Schur decomposition; Laplace transform; fractional calculus
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Popolizio, M. On the Matrix Mittag–Leffler Function: Theoretical Properties and Numerical Computation. Mathematics 2019, 7, 1140.

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