Chaos in a three-cell population cancer model with variable-order fractional derivative with power, exponential and Mittag-Leffler memories.

In this work, a three-dimensional cancer model which includes the interactions between tumor cells, healthy tissue cells, and activated immune system cells was considered via Liouville–Caputo, Caputo–Fabrizio, Atangana–Baleanu, and fractional conformable derivative. We show a numerical method based on two-step Lagrange polynomial interpolation to achieve numerical approximations to these derivatives. Besides, also we analyze the dynamics observed via sensitivity to initial conditions, Lyapunov exponent estimation, square sum error, and phase-space diagrams. Novel attractors were obtained and all of them depicted novel chaotic behaviors by choosing a fractional variable-order. [ABSTRACT FROM AUTHOR]