  Given the Caputo-type fractional differential equation $D^\alpha y(t) = f(t,
y(t))$ with $\alpha \in (1, 2)$, we consider two distinct solutions $y_1, y_2
\in C[0,T]$ to this equation subject to different sets of initial conditions.
In this framework, we discuss nontrivial upper and lower bounds for the
difference $|y_1(t) - y_2(t)|$ for $t \in [0,T]$. The main emphasis is on
describing how such bounds are related to the differences of the associated
initial values.
