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 \left( s,m\right) -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.

Keywords:

Simpson's type inequalities , (s , m)-convex function , Caputo-Fabrizio fractional integral operators , power-mean inequality , Special means , Modified Bessel function , error bounds , q-digamma functions , Matrix inequality