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.
Munir et al. (Thu,) studied this question.