Distribution of Zeros of the Mittag-Leffler Function

The Mittag-Leffler function, which is a generalization of the exponential function, occurs naturally in the solution of physical problems involving fractional differential equations. The zeros of the Mittag-Leffler functions play a significant role in the dynamics solutions. Complete and correct information about the distribution of zeros has not yet been available. A systematic analysis of the zeros of E$_{\alpha ,\alpha }$(z) has been carried out and an iteration formula for the number of zeros for arbitrary alpha has been obtained.