  In this work we characterize the escape of orbits from the phase space of the
Riemann-Liouville (RL) fractional standard map (fSM). The RL-fSM, given in
action-angle variables, is derived from the equation of motion of the kicked
rotor when the second order derivative is substituted by a RL derivative of
fractional order $\alpha$. Thus, the RL-fSM is parameterized by $K$ and
$\alpha\in(1,2]$ which control the strength of nonlinearity and the fractional
order of the RL derivative, respectively. Indeed, for $\alpha=2$ and given
initial conditions, the RL-fSM reproduces Chirikov's standard map. By computing
the survival probability $P_{\text{S}}(n)$ and the frequency of escape
$P_{\text{E}}(n)$, for a hole of hight $h$ placed in the action axis, we
observe two scenarios: When the phase space is ergodic, both scattering
functions are scale invariant with the typical escape time
$n_{\text{typ}}=\exp\langle \ln n \rangle \propto (h/K)^2$. In contrast, when
the phase space is not ergodic, the scattering functions show a clear
non-universal and parameter-dependent behavior.
