The numerical study of the cancer model in biological science

The incorporation of fractional calculus into the study of biological models represents a significant advancement in addressing health-related issues affecting humans. Utilizing fractional definitions and associated mathematical techniques is instrumental in comprehending these models. This work presents novel numerical solutions for a cancer model, employing the generalized Caputo (G-C) fractional derivative as well as the fractional conformable and β-conformable derivatives in the Liouville–Caputo (LC) sense. The model under consideration describes the interplay between tumor cells, healthy cells, and activated immune cells. The numerical solutions are presented using an adaptive predictor-corrector numerical approach for the generalized Caputo derivative and an Adams–Moulton-type numerical scheme for the arbitrary-order conformable derivatives. We present a range of simulations featuring various parameter values for α and β, which help illustrate the behavior of tumor and immune cells.