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Matrix Mittag‑Leffler function in fractional systems and its computation

Matychyn I., Onyshchenko V.

Bulletin of the Polish Academy of Sciences. Technical Sciences

2018

Vol. 66, nr 4

495--500

Matrix Mittag‑Leffler functions play a key role in numerous applications related to systems with fractional dynamics. That is why the methods for computing the matrix Mittag‑Leffler function are so important. The matrix Mittag‑Leffler function is a generalization of matrix exponential function. This implies that some of numerous existing methods for computing the matrix exponential can be adapted for matrix Mittag‑Leffler functions as well. Unfortunately, the technique of scaling and squaring, widely used in computing of the matrix exponential, cannot be applied to matrix Mittag‑Leffler functions, as the latter do not possess the semigroup property. Here we describe a method of computing the matrix Mittag‑Leffler function based on the Jordan canonical form representation. This method is implemented with Matlab code [1].

Derivatives of Markov kernels and their Jordan decomposition

Heidergott B., Hordijk A., Weisshaupt H.

Journal of Applied Analysis

2008

Vol. 14, nr 1

13-26

We study a particular class of transition kernels that stems from differentiating Markov kernels in the weak sense. Sufficient conditions are established for this type of kernels to admit a Jordan-type decomposition. The decomposition is explicitly constructed.