Defterli, OzlemTang, YifaBaleanu, DumitruArshad, SadiaSaleem, Iram2023-01-042025-09-182023-01-042025-09-182021Arshad, 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. 12.0031-89491402-4896https://doi.org/10.1088/1402-4896/ac1e5ahttps://hdl.handle.net/20.500.12416/10828Arshad, Sadia/0000-0001-9085-5915This 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 ModelChaosArticle10.1088/1402-4896/ac1e5a2-s2.0-85115176054