  We prove new estimates of the Caputo derivative of order $\alpha \in (0,1]$
for some specific functions. The estimations are shown useful to construct
Lyapunov functions for systems of fractional differential equations in biology,
based on those known for ordinary differential equations, and therefore useful
to determine the global stability of the equilibrium points for fractional
systems. To illustrate the usefulness of our theoretical results, a fractional
HIV population model and a fractional cellular model are studied. More
precisely, we construct suitable Lyapunov functionals to demonstrate the global
stability of the free and endemic equilibriums, for both fractional models, and
we also perform some numerical simulations that confirm our choices.
