Majorization-Based Conticrete Inequalities Involving the Caputo-Fabrizio Fractional Operators with Applications to Modified Bessel Functions and Special Means

Abstract

The Hermite-Hadamard inequality is universally recognized as a highly influential inequality in mathematics. Nowadays, researchers are actively engaged in exploring its various improvements, generalizations and refinements. This article focuses on determining the results of Hermite-Hadamard-Mercer type in conticrete settings within a fractional framework. The approach combines the ideas of majorization, convexity, and Caputo-Fabrizio fractional operators. New weighted versions are also presented by employing certain monotonic tuples together with weighted majorized Jensen-Mercer inequalities. In addition, an integral identity is established for a differentiable function. This identity is further applied to obtain estimates for the discrepancy in terms related to the major result. The obtained bounds rely on the convex nature of |f′|, |f′|^q, (1 < q), along with power mean, Hölder, and Young’s inequalities. The paper further demonstrates applications of the main findings to modified Bessel functions and special means. Several existing results are recovered as special cases, while new inequalities are also established.