Journal
APPLIED MATHEMATICS AND COMPUTATION
Volume 338, Issue -, Pages 733-738Publisher
ELSEVIER SCIENCE INC
DOI: 10.1016/j.amc.2018.06.037
Keywords
Matrix Mittag-Leffler function; Matrix exponential; Matrix function
Categories
Funding
- Robat Karim branch, Islamic Azad University, Tehran, Iran
- ISR-University of Coimbra - Fundacao para a Ciencia e a Tecnologia (FCT) [UID/EEA/00048/2013]
- Fundação para a Ciência e a Tecnologia [UID/EEA/00048/2013] Funding Source: FCT
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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. (C) 2018 Elsevier Inc. All rights reserved.
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