CERTAIN NEW WEIGHTED YOUNG- AND PÓLYA–SZEGÖ-TYPE INEQUALITIES FOR UNIFIED FRACTIONAL INTEGRAL OPERATORS VIA AN EXTENDED GENERALIZED MITTAG-LEFFLER FUNCTION WITH APPLICATIONS

Wengui Yang
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Wengui Yang: Ministry of Public Education, Sanmenxia Polytechnic, Sanmenxia 472000, P. R. China2School of Applied Engineering, Henan University of Science and Technology, Sanmenxia 472000, P. R. China

FRACTALS (fractals), 2022, vol. 30, issue 06, 1-37

Abstract: This paper investigates certain new weighted Young- and Pólya–Szegö-type inequalities for unified fractional integral operators via an extended generalized Mittag-Leffler function. A large quantity of usable classical inequalities in the literature are included in the main results of this paper. Meanwhile, two types of new generalized weighted fractional integral operators are introduced to establish some new weighted Young- and Pólya–Szegö-type inequalities. As applications, several estimates of Chebyshev-type weighted unified fractional integral inequalities with two unknown functions are obtained by employing the Heaviside unit step function. Finally, some relations between main results and known inequalities for different kinds of fractional integral operators are provided.

Keywords: Young Inequality; Pólya–Szegö Inequality; Unified Fractional Integral Operators; Mittag-Leffler Function; Chebyshev Functional; Heaviside Unit Step Function (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1142/S0218348X22501067

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