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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Veröffentlicht in:Applied mathematics and computation Jg. 338; S. 733 - 738
Hauptverfasser: Sadeghi, Amir, Cardoso, João R.
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Elsevier Inc 01.12.2018
Schlagworte:
Matrix exponential
Matrix function
Matrix Mittag-Leffler function
Matrix Mittag-Leffler function
Matrix function
Matrix exponential
ISSN:0096-3003, 1873-5649
Online-Zugang:Volltext
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Zusammenfassung: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