Monotonicity criterion and integrals formulas for the Mittag-Leffler function with applications

Khaled Mehrez
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Khaled Mehrez: University of Kairouan, 3100, University of Kairouan

Indian Journal of Pure and Applied Mathematics, 2022, vol. 53, issue 2, 392-404

Abstract: Abstract In this paper, we prove the monotonicity property of the ratios of Mittag-Leffler functions. As applications, new functional inequalities (such as Turán type inequalities) for the Mittag-Leffler function are obtained. Moreover, geometrical convexity and log-concavity properties for some classes of functions related to the Mittag-Leffler function are researched. Furthermore, new formulas and inequalities for some integrals involving the Mittag-Leffler functions are established.

Keywords: Mittag-Leffler function; Monotonicity; convexity; functional inequality; Turán-type inequalities; Integral; 30C45; 30D15; 33C10 (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s13226-021-00212-7

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