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On Pólya-Szegő and Chebyshev types inequalities involving the Riemann-Liouville fractional integral operators. (English) Zbl 1337.26034

Summary: In this paper, we investigate some new Pólya-Szegő type integral inequalities involving the Riemann-Liouville fractional integral operator, and use them to prove some fractional integral inequalities of Chebyshev type, concerning the integral of the product of two functions and the product of two integrals. Certain special cases are also considered. Finally, examples for constructing the bounding functions are also given.

MSC:

26D10 Inequalities involving derivatives and differential and integral operators
26A33 Fractional derivatives and integrals
26D15 Inequalities for sums, series and integrals
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