Modified Versions of Fractional Inequalities via Double Integral Operators with Coordinated Convexity

Abstract

Integral inequalities are of great importance in both theoretical and applied analysis. There is no doubt that inequalities aim to develop various mathematical techniques. Therefore, in order to prove the accuracy and uniqueness of such mathematical techniques, it is necessary to find explicit inequalities. The behavior and properties of the convexity of the functions are of great importance in the field of inequalities. This paper aims to introduce a new class of coordinated convexity, pre-invexities, modify some well-known fractional inequalities, and its refinements by implementation of two-dimensional fractional integral operators. We present a novel form of Hermite-Hadamard (H-H) and trapezoidal-type fractional two-dimensional integral inequalities for coordinated convex and pre-invex functions, grounded in the $h$-Godunova-Levin framework. Moreover, we deduce some corollaries from the main results, which are the famous inequalities in the previously published articles.