On Fractional Integral Inequalities of Riemann Type for Composite Convex Functions and Applications

In this study, we apply fractional calculus on certain convex functions and derive many novel mean-type inequalities by employing fractional calculus and convexity theory. In order to investigate fractional mean inequalities, we first build an identity in this study. Then, with its help, we derive many mean-type inequalities and estimate the error of HH inequality using a generalized version of RL-fractional integrals and certain classes of convex functions. The results obtained are validated by taking specific functions. Many mean-type inequalities that exist in the literature are generalized by the main results of this study.

Automated summary

In this study, we apply fractional calculus and convexity theory to certain convex functions, deriving novel mean-type inequalities. By establishing an identity, we investigate fractional mean inequalities and estimate the error of the HH inequality using RL-fractional integrals and convex functions. Specific functions are used for validation, and the main results of this study generalize many existing mean-type inequalities in the literature.