Some notes on properties of the matrix Mittag-Leffler function

We have come across with publications where some properties of the matrix exponential were incorrectly extended to the matrix Mittag-Leffler function, and then used as a key tool to solve certain linear matrix fractional differential equations. The main purpose of these notes is to give some clarifi...

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Bibliographic Details
Published in:	Applied mathematics and computation Vol. 338; pp. 733 - 738
Main Authors:	Sadeghi, Amir, Cardoso, João R.
Format:	Journal Article
Language:	English
Published:	Elsevier Inc 01.12.2018
Subjects:	Matrix exponential Matrix function Matrix Mittag-Leffler function Matrix Mittag-Leffler function Matrix function Matrix exponential
ISSN:	0096-3003, 1873-5649
Online Access:	Get full text
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Summary:	We have come across with publications where some properties of the matrix exponential were incorrectly extended to the matrix Mittag-Leffler function, and then used as a key tool to solve certain linear matrix fractional differential equations. The main purpose of these notes is to give some clarifications on properties of the matrix Mittag-Leffler function, by explaining in detail why some identities do not hold and by providing a list of (valid) properties of this function. A sufficient condition to identify very special cases of pairs of matrices satisfying the semigroup property is given as well as examples illustrating the results.
ISSN:	0096-3003 1873-5649
DOI:	10.1016/j.amc.2018.06.037