On Bullen-Type Inequalities for Fractional Integrals with Exponential Kernels

Abstract

In this paper, we investigate the Bullen inequality in the context of fractional integrals with exponential kernels. Building upon the foundational works in the field, we first introduce a new integral identity. From this identity, we derive several novel Bullen-type inequalities for differentiable convex functions. To validate our theoretical findings, we provide a numerical example along with graphical representations, demonstrating the accuracy and applicability of our results. The results obtained are not only new for the fractional integrals considered in our study, but as \(\alpha\) approaches 1, we also derive additional novel results for the classical integral.

Keywords

• fractional integrals with exponential kernels
• bullen-type inequalities
• convex functions
• holder's inequality
• power mean inequality