Representation of the Mittag-Leffler function through the exponential functions in the case of rational derivatives

Abstract: In this paper the Mittag-Leffler function is given through the exponential functions for any rational derivatives of m/n order, where m<n, n\>1 are natural irreducible numbers (if n=1 then m is also equal to unity). Unlike the previous papers the given formulas do not contain integrals.