Fractional integral Chebyshev inequality without synchronous functions condition

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].