  In this work, we analyze the effects of fractional derivatives in the chaotic
dynamics of a cancer model. We begin by studying the dynamics of a standard
model, {\it i.e.}, with integer derivatives. We study the dynamical behavior by
means of the bifurcation diagram, Lyapunov exponents, and recurrence
quantification analysis (RQA), such as the recurrence rate (RR), the
determinism (DET), and the recurrence time entropy (RTE). We find a high
correlation coefficient between the Lyapunov exponents and RTE. Our simulations
suggest that the tumor growth parameter ($\rho_1$) is associated with a chaotic
regime. Our results suggest a high correlation between the largest Lyapunov
exponents and RTE. After understanding the dynamics of the model in the
standard formulation, we extend our results by considering fractional
operators. We fix the parameters in the chaotic regime and investigate the
effects of the fractional order. We demonstrate how fractional dynamics can be
properly characterized using RQA measures, which offer the advantage of not
requiring knowledge of the fractional Jacobian matrix. We find that the chaotic
motion is suppressed as $\alpha$ decreases, and the system becomes periodic for
$\alpha \lessapprox 0.9966$. We observe limit cycles for $\alpha \in
(0.9966,0.899)$ and fixed points for $\alpha<0.899$. The fixed point is
determined analytically for the considered parameters. Finally, we discover
that these dynamics are separated by an exponential relationship between
$\alpha$ and $\rho_1$. Also, the transition depends on a supper transient which
obeys the same relationship.
