Enumeration of the real zeros of the Mittag-Leffler function Eα(z), 1<α<2

The Mittag-Leffler function E-alpha(z), which is a generalization of the exponential function, arises frequently in the solutions of physical problems described by differential and/or integral equations of fractional order. Consequently, the zeros of E-alpha(z) and their distribution are of fundamental importance and play a significant role in the dynamic solutions. The Mittag-Leffler function E-alpha(z) is known to have a finite number of real zeros in the range 1 <alpha < 2 which is applicable for many physical problems. What has not been known is the exact number of real zeros of E-alpha(z) for a given value of a in this range. An iteration fomula is derived for calculating the number of real zeros of E-alpha(z) for any value of alpha in the range 1 <alpha < 2 and some specific results are tabulated.