Turán type inequalities for classical and generalized Mittag-Leffler functions

Abstract: In this paper some Tur\'an type inequalities for classical and generalized Mittag-Leffler functions are considered. The method is based on proving monotonicity for special ratio of sections for series of Mittag-Leffler functions. Some applications are considered to Lazarevi\'c and Wilker-type inequalities for classical and generalized Mittag-Leffler functions. At the end some open problems are formulated.