On Caputo–Fabrizio Fractional Integral Inequalities of Hermite–Hadamard Type for Modified $h$-Convex Functions

Abstract

The theory of convex functions plays an important role in engineering and applied mathematics. The Caputo–Fabrizio fractional derivatives are one of the important notions of fractional calculus. The aim of this paper is to present some properties of Caputo–Fabrizio fractional integral operator in the setting of h -convex function. We present some new Caputo–Fabrizio fractional estimates from Hermite–Hadamard-type inequalities. The results of this paper can be considered as the generalization and extension of many existing results of inequalities and convex functions. Moreover, we also present some application of our results to special means of real numbers.

Inequalities presenting error bounds for trapezoidal formula using Caputo-Fabrizio integrals via convex functions with graphical depiction

“…In 2020, Wang et al provided inequalities for modified h-convex functions [33]. In 2020, Butt et al gave inequalities for exponential s-convex and exponential (s, m)-convex functions involving Caputo fractional derivative [3,4].…”

A Study of Some New Hermite–Hadamard Inequalities via Specific Convex Functions with Applications

“…The key characteristic of this operator is best described as a real power transformed into an integer through the Laplace transformation, thereby facilitating the straightforward derivation of exact solutions for various problems. Xiaobin Wang et al [23] presented the Hermite-Hadmard-type inequality for modified h-convex functions utilizing a Caputo-Fabrizio integral operator. Butt et al [24] exponentially obtained different inequalities for s-and (s,m)-convex functions using Caputo fractional integrals and derivatives.…”

Error Bounds for Fractional Integral Inequalities with Applications

“…Recently, a few generic and midpoint-shaped fractional inequalities were explored by Hyder et al (see [27]). Using the well-known fractional operator (Caputo-Fabrizio), Xiaobin wang et al [28] proved the Hermite-Hadamarditype inequalities for modified h-convexifunctions. Abbasi demonstrated the novel versionsiof Hermite-Hadamard type inequalities for s-convex functions utilizing the (Caputo-Fabrizio integral operator).…”