The Mittag-Leffler function Eα(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 Eα (z) and their distribution are of fundamental importance and play a significant role in the dynamic solutions. The Mittag- Leffler function E (z) is known to have a finite number of real zeros in the range 1 < α > 2 which is applicable for many physical problems. What has not been known is the exact number of real zeros of Eα (z) for a given value of α in this range. An iteration formula is derived for calculating the number of real zeros of Eα(z) for any value of α in the range 1 < α > 2 and some specific results are tabulated. Key words Mittag-Leffler functions, zeros, fractional calculus.
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Hanneken, J.W., Vaught, D.M., Achar, B.N.N. (2007). Enumeration of the Real Zeros of the Mittag-Leffler Function Eα(z), 1 <α< 2. In: Sabatier, J., Agrawal, O.P., Machado, J.A.T. (eds) Advances in Fractional Calculus. Springer, Dordrecht. https://doi.org/10.1007/978-1-4020-6042-7_2
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