Some Parameterized Simpson-Mercer Type Inequalities for General Fractional Operators

Abstract

This paper establishes new parameterized Simpson Mercer-type inequalities for functions of two variables within the framework of generalized fractional integral operators. By deriving novel integral identities for twice partially differentiable mappings, we provide several generalized forms for free parameters. Our results extend and unify a wide range of existing fractional integral inequalities, including those based on the Riemann-Liouville, k-Riemann-Liouville, and other fractional operators. These findings enrich the theory of integral inequalities and offer new tools for applications in convex analysis, numerical integration, and fractional calculus.