Chebyshev-Type Inequalities via a Novel Fractional Integral Operator

The novel fractional integral operator presented in this paper unifies and generalizes several existing fractional calculus operators. By applying this operator, we provide a significant extension of the classical results to the fractional setting by establishing a Chebyshev-type integral inequality for the synchronous functions. The primary inequality offers a flexible way to examine how functions behave when fractional integration is applied. The suggested approach is consistent with the existing results in the literature, as evidenced by the derivation of several corollaries and special cases as applications. The developed findings open up new directions for mathematical analysis study and their applications in practical sciences, while also adding to the expanding theory of fractional inequalities. The study discussed in this paper advances the inequality theory and fractional calculus.