Further Integral Inequalities through Some Generalized Fractional Integral Operators

Abstract

In this article, we utilize recent generalized fractional operators to establish some fractional inequalities in Hermite–Hadamard and Minkowski settings. It is obvious that many previously published inequalities can be derived as particular cases from our outcomes. Moreover, we articulate some flaws in the proofs of recently affiliated formulas by revealing the weak points and introducing more rigorous proofs amending and expanding the results.

Enlarged integral inequalities through recent fractional generalized operators

“…These inequalities concern the Hermite-Hadamard and Minkowski inequalities. Our outcomes can be compared by the previous results established in [3,12,22]. The inequalities obtained in these references can be derived as particular cases.…”

“…In the context of the generalized fractional theta-obedient integral, a variety of research directions related to integral inequalities can be examined in equation (12). More research on the Hermite-Hadamard inequality with differentiable h-convex functions [31], Hermite-Hadamard inequality for s-convex functions [29], the binary Brunn-Minkowski inequality [17], and other topics are predicted under this operator.…”

“…In this study, we establish the Hermite-Hadamard and Minkowski inequalities in the context of newly generalized fractional integral operators. We examine some specific cases arising from our findings in this section by presenting some particular examples of our fractional integral operator described by equation (12) as the following cases.…”

“…Also, Nisar et al [22] employed the Minkowski and Hermite-Hadamard inequalities to expand the results of Dahmani [4] and proposed a more powerful integral inequality. Hyder et al [12] utilized some generalized fractional integrals to examine specific fractional-order inequalities in Let us start with the traditional Hermite-Hadamard inequality:…”

New Versions of Midpoint Inequalities Based on Extended Riemann–Liouville Fractional Integrals

“…The inequality of Hermite-Hadamard is the first result of convex mappings, and has a straightforward geometric demonstration and a variety of applications, making it the most interesting inequality. For more details concerning the Hermite-Hadamard inequality, see [13][14][15]. Using Riemann-Liouville fractional integrals and convex analysis, Sarikaya et al [16] recently proved many Hermite-Hadamard and trapezoidal inequalities.…”