Matrix Mittag-Leffler function in fractional systems and its computation

摘要

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].