The left Non-Conformable-Mercer fractional Hermite-Hadamard type inequalities using convex functions

Abstract

This paper introduces a significant advancement in the field of fractional integral inequalities by establishing new Hermite-Hadamard (H-H) type inequalities for convex functions, specifically of the Jensen-Mercer kind, within the framework of non-conformable fractional calculus. The core of our approach leverages the support line property of convex functions to derive a foundational fractional (H-H)-Mercer inequality. From this cornerstone result, we develop new integral identities related to non-conformable fractional operators. These identities serve as powerful tools to prove a suite of associated trapezoidal and midpoint type inequalities that provide explicit bounds for the approximation error. This research is important as it deepens the link between convex analysis and fractional calculus, offering more versatile tools for analyzing the behavior of convex functions under generalized integral operators. The results are expected to have applications in various domains where fractional modeling and optimization are crucial, such as mathematical physics, engineering systems, and economic modeling, providing refined methods for approximation anda error estimation.a