  We analyze the nonlinear Helmholtz oscillator in the presence of fractional
damping, a characteristic feature in several physical situations. In our
specific scenario, as well as in the non-fractional case, for large enough
excitation amplitudes, all initial conditions are escaping from the potential
well. To address this, we incorporate the phase control technique into a
parametric term, a feature commonly encountered in real-world situations. In
the non-fractional case it has been shown that, a phase difference of
{\phi_{OPT}} \simeq {\pi}, is the optimal value to avoid the escapes of the
particles from the potential well. Here, our investigation focuses on
understanding when particles escape, considering both the phase difference
{\phi} and the fractional parameter {\alpha} as control parameters. Our
findings unveil the robustness of phase control, as evidenced by the consistent
oscillation of the optimal {\phi} value around its non-fractional counterpart
when varying the fractional parameter. Additionally, our results underscore the
pivotal role of the fractional parameter in governing the proportion of bounded
particles, even when utilizing the optimal phase.
