New extensions of Chebyshev type inequalities using generalized Katugampola integrals via P´olya-Szeg¨o inequality

Abstract

A number of Chebyshev type inequalities involving various fractional integraloperators have, recently, been presented. In this work, motivated essentiallyby the earlier works and their applications in diverse research subjects, we establishsome new P´olya-Szeg¨o inequalities involving generalized Katugampolafractional integral operator and use them to prove some new fractional Chebyshevtype inequalities which are extensions of the results in the paper: [OnP´olya-Szeg¨o and Chebyshev type inequalities involving the Riemann-Liouvillefractional integral operators, J. Math. Inequal, 10(2) (2016)].