Enumeration of the real zeros of the Mittag-Leffler function
. (English) Zbl 1124.33020
Sabatier, J. (ed.) et al., Advances in fractional calculus. Theoretical developments and applications in physics and engineering. Dordrecht: Springer (ISBN 978-1-4020-6041-0/hbk; 978-1-4020-6042-7/e-book). 15-26 (2007).
Summary: The Mittag-Leffler function , 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 and their distribution are of fundamental importance and play a significant role in the dynamic solutions. The Mittag-Leffler function is known to have a finite number of real zeros in the range which is applicable for many physical problems. What has not been known is the exact number of real zeros of for a given value of in this range. An iteration formula is derived for calculating the number of real zeros of for any value of in the range and some specific results are tabulated.
|33E12||Mittag-Leffler functions and generalizations|
|26A33||Fractional derivatives and integrals (real functions)|