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In this paper certain Pólya-Szegö type integral inequalities due to Karamata’s estimations of the Chebyshev quotient are presented. Those inequalities include an extended generalized Mittag-Leffler function with the corresponding fractional integral operator, and from them, some fractional integral inequalities of Chebyshev type are obtained. Also, several known results are improved. Mathematics subject classification (2010): 26A33, 26D10, 33E12.

Pólya-Szegö and Chebyshev types inequalities via an extended generalized Mittag-Leffler function