Abstract. By using the Riemann-Liouville fractional integral operator, we establish new weighted results of Chebyshev inequality type. Other integral inequalities of fractional order are also proved. Some classical results can be deduced as special cases. MSC 2010. 26D10, 26A33.

In this paper, we use the Riemann-Liouville fractional integrals to establish some new integral inequalities related to the Chebyshev inequality in the case where the synchronicity of the given functions is replaced by another condition. This paper generalises some recent results in the paper of [C.P. Niculescu and I. Roventa: An extension of Chebyshev’s algebraic inequality, Math. Reports, 2013].

In this paper, we present new generalizations for some integral results related to Hardy inequalities. For our results, some recent results of Hardy type and other interesting inequalities of integer order of integration can be deduced as some special cases.

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