Matrix Mittag-Leffler function in fractional systems and its computation

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].