Analysis On Simpson's Type Inequalities Through Generalized Convexity with Applications

Fractional operators and integral inequalities have become a focal point of research due to their applications in mathematics, physics, engineering, and applied sciences. This paper introduces a new identity for the Caputo-Fabrizio fractional integral operators. Employing the Peano kernel method, we derive Simpson's type inequalities for ( s,m)-convex functions through twice-differentiable functions, accompanied by graphical illustrations to analyze their behavior. Several new corollaries are established, with insightful remarks enhancing their interpretation.Additionally, applications to special means, q-digamma functions, modified Bessel function, Simpson's formula, matrix inequality, and midpoint formula are explored, underscoring the utility and adaptability of these results across various mathematical and applied domains.