Certain Weighted Fractional Integral Inequalities Involving Convex Functions

Abstract

A comprehensive examination of applied sciences and their advancement necessitates an expansion of analytical studies. Our objective in this article is to unveil and present a fresh perspective on weighted integral inequalities by introducing the concept of the weighted proportional Hadamard fractional integral operator. To achieve this generalization, we have used positive and continuous functions, while some of the functions used during our generalization of these inequalities must fulfill the condition of being convex over a certain period that represents the range of functions used for the generalization. Additionally, we establish some novel inequalities using this fractional integral operator. We also delve into specific instances of the findings we present. This study significantly contributes to the literature by bridging gaps in the understanding of fractional integrals and their relationship with convex functions, thereby paving the way for future research in this dynamic area.