Arshad, SadiaSaleem, IramDefterli, ÖzlemTang, YifaBaleanu, Dumitru2023-01-042023-01-042021Arshad, Sadia...et al. (2021). "Simpson's method for fractional differential equations with a non-singular kernel applied to a chaotic tumor model", PHYSICA SCRIPTA, Vol. 96, No. 12.0031-89491402-4896http://hdl.handle.net/20.500.12416/6015This manuscript is devoted to describing a novel numerical scheme to solve differential equations of fractional order with a non-singular kernel namely, Caputo-Fabrizio. First, we have transformed the fractional order differential equation to the corresponding integral equation, then the fractional integral equation is approximated by using the Simpson's quadrature 3/8 rule. The stability of the proposed numerical scheme and its convergence is analyzed. Further, a cancer growth Caputo-Fabrizio model is solved using the newly proposed numerical method. Moreover, the numerical results are provided for different values of the fractional-order within some special cases of model parameters.eninfo:eu-repo/semantics/closedAccessFractional Operator With the Non-Singular KernelNumerical ApproximationStability AnalysisConvergence AnalysisTumor ModelChaosArticle961210.1088/1402-4896/ac1e5a