Generalization of different type integral inequalities for s-convex functions via fractional integrals

TL;DR

This paper develops new estimates for integral inequalities involving s-convex functions using fractional integrals, extending classical inequalities like Hermite-Hadamard and Simpson.

Contribution

It introduces a general integral identity for twice differentiable functions and applies it to derive novel bounds for s-convex functions via fractional integrals.

Findings

New bounds for Hermite-Hadamard type inequalities

Extensions of Simpson type inequalities for s-convex functions

Use of Riemann-Liouville fractional integrals in inequality estimates

Abstract

In this paper, a general integral identity for twice differentiable functions is derived. By using of this identity, the author establish some new estimates on Hermite-Hadamard type and Simpson type inequalities for s-convex via Riemann Liouville fractional integral.