Multiplicative fractional Simpson-like inequalities for multiplicatively twice-differentiable s-convex functions

Abstract

This paper studies multiplicative fractional Simpson-like inequalities, which are commonly employed in the error analysis of quadrature formulas within the multiplicative Riemann–Liouville (RL) fractional framework. First, we develop a multiplicative fractional identity for multiplicatively twice-differentiable functions. Utilizing the introduced identity, we formulate Simpson-like inequalities under the following two conditions: (i) satisfies multiplicative s-convexity, or (ii) is s-convex for q > 1. To validate and illustrate the presented inequalities, we finally provide numerical examples and graphical depictions, which clearly support the theoretical results.