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

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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.

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Authors and Affiliations

  1. Department of Mathematics, Kairouan Preparatory Institute for Engineering Studies, University of Kairouan, 3100, University of Kairouan, Kairouan, Tunisia

    Khaled Mehrez

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  1. Khaled Mehrez
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Communicated by T. S. S. R. K. Rao.

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Mehrez, K. Monotonicity criterion and integrals formulas for the Mittag-Leffler function with applications. Indian J Pure Appl Math 53, 392–404 (2022). https://doi.org/10.1007/s13226-021-00212-7

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  • DOI: https://doi.org/10.1007/s13226-021-00212-7

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