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

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

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 aime...

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Bibliographic Details
Main Author: Marina Popolizio
Format: Article
Language:English
Published: MDPI AG 2019-11-01
Series:Mathematics
Subjects:
mittag–leffler function
matrix function
schur decomposition
laplace transform
fractional calculus
Online Access:https://www.mdpi.com/2227-7390/7/12/1140
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spelling doaj-b9fc8f277a0b4a66a0b27c95389a43f42020-11-25T02:26:18ZengMDPI AGMathematics2227-73902019-11-01712114010.3390/math7121140math7121140On the Matrix Mittag–Leffler Function: Theoretical Properties and Numerical ComputationMarina Popolizio0Department of Electrical and Information Engineering, Polytechnic University of Bari, Via E. Orabona n.4, 70125 Bari, ItalyMany 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.https://www.mdpi.com/2227-7390/7/12/1140mittag–leffler functionmatrix functionschur decompositionlaplace transformfractional calculus
collection DOAJ
language English
format Article
sources DOAJ
author Marina Popolizio
spellingShingle Marina Popolizio
On the Matrix Mittag–Leffler Function: Theoretical Properties and Numerical Computation
Mathematics
mittag–leffler function
matrix function
schur decomposition
laplace transform
fractional calculus
author_facet Marina Popolizio
author_sort Marina Popolizio
title On the Matrix Mittag–Leffler Function: Theoretical Properties and Numerical Computation
title_short On the Matrix Mittag–Leffler Function: Theoretical Properties and Numerical Computation
title_full On the Matrix Mittag–Leffler Function: Theoretical Properties and Numerical Computation
title_fullStr On the Matrix Mittag–Leffler Function: Theoretical Properties and Numerical Computation
title_full_unstemmed On the Matrix Mittag–Leffler Function: Theoretical Properties and Numerical Computation
title_sort on the matrix mittag–leffler function: theoretical properties and numerical computation
publisher MDPI AG
series Mathematics
issn 2227-7390
publishDate 2019-11-01
description 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.
topic mittag–leffler function
matrix function
schur decomposition
laplace transform
fractional calculus
url https://www.mdpi.com/2227-7390/7/12/1140
work_keys_str_mv AT marinapopolizio onthematrixmittaglefflerfunctiontheoreticalpropertiesandnumericalcomputation
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