Analytical and Numerical Study of Newton-Type Inequalities for Differentiable $s$-Type Convex Functions via Riemann-Liouville Fractional Integrals

This article investigates fractional Newton-type integral inequalities within the framework of $s$-type convexity. Employing a fundamental identity for Riemann-Liouville fractional integrals, new estimates are derived for functions whose derivatives satisfy $s$-type convexity conditions. Various test functions are examined, and graphical visualizations are provided to illustrate the effectiveness of the proposed estimates. It is emphasized that the established results extend the classical Newton-type inequalities to a wider class of functions, which are not necessarily convex. The outcomes of this investigation are expected to inspire further studies involving alternative fractional operators and broader convexity classes.