atangana–baleanu–caputo (abc), caputo-fabrizio (cf), and caputo fractional derivative approaches in fuzzy time fractional cancer tumor growth models

This article introduces a new approach for solving a time-fractional cancer tumor model using caputo, caputo-fabrizio (cf), and atangana-baleanu-caputo (abc) fractional derivatives, accounting for varying net-killing rates of cancer cells in an uncertain environment. the model with the caputo derivative is initially tackled using an explicit finite difference method (efdm) with a fully time-dependent net killing rate. approximate solutions for two different net death rates are obtained using the sumudu transformation (st) combined with the adomian decomposition method (adm), providing more accurate approximations than the efdm. the model's behavior is analyzed with 2d and 3d visualizations. convergence and error analysis of the method for the caputo fractional derivative have been performed. the adm provides reliable approximations for fractional models with fuzzy parameters, outperforming the efdm by achieving lower absolute errors. the results exhibit symmetric lower and upper approximations around zero, effectively capturing the fuzzy nature of the solution.  all methods converge to zero at higher cuts in fuzzy triangular numbers, i.e. v = 1.