In this paper, we consider the integral operators corresponding to the non-singular fractional derivative introduced by Caputo and Fabrizio in 2015. Using the Caputo-Fabrizio fractional integrals, new Hermite-Hadamard type inequalities are established for strongly (s;m)-convex functions. The obtained results not only generalize several classical inequalities available in the literature but also highlight the advantages of the non-singular kernel structure in the study of strongly convex mappings. Furthermore, the theoretical findings are supported by various applications. In addition, the graphs prepared to visualize the results clearly demonstrate the potential of the proposed approach in both theoretical and applied mathematics. $CF_w^a P(x) = \frac{1}{M(a)} P(w) + \frac{M(a)}{a-w} \int_w^x \frac{1}{P(x) dx} > w$; $CF_z^b P(x) = \frac{1}{M(b)} P(z) + \frac{M(b)}{b-z} \int_z^x \frac{1}{P(x) dx} < z$