Arshad, SadiaSaleem, IramAkgul, AliHuang, JianfeiTang, YifaEldin, Sayed M.2024-12-242024-12-2420232473-6988https://doi.org/10.3934/math.2023481https://hdl.handle.net/20.500.12604/8406In this paper, a unique and novel numerical approach-the fractional-order Caputo-Fabrizio derivative in the Caputo sense-is developed for the solution of fractional differential equations with a non-singular kernel. After converting the differential equation into its corresponding fractional integral equation, we used Simpson's 1/3 rule to estimate the fractional integral equation. A thorough study is then conducted to determine the convergence and stability of the suggested method. We undertake numerical experiments to corroborate our theoretical findings.eninfo:eu-repo/semantics/openAccessfractional differential equationnon-singular operatornumerical approximationstability analysisconvergence analysisArticle8495359556Q1WOS:000995999000003Q12-s2.0-8514846225210.3934/math.2023481