Some notes on properties of the matrix Mittag-Leffler function
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摘要
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.
论文关键词:Matrix Mittag-Leffler function,Matrix exponential,Matrix function
论文评审过程:Received 18 November 2017, Revised 4 June 2018, Accepted 17 June 2018, Available online 24 July 2018, Version of Record 24 July 2018.
论文官网地址:https://doi.org/10.1016/j.amc.2018.06.037