Purpose <p>In this paper, we present a Ψ-Hilfer fractional generalization of the Van der Pol–Nonlinear Energy Sink (VDP–NES) system in order to investigate the effect of memory and kernel-dependent time scaling on the use of non-linear oscillators for vibration attenuation.</p> Methods <p>Starting from a classical mechanical implementation of the VDP–NES system, we derive the equations of motion of the oscillator in terms of the Ψ-Hilfer fractional derivative. Due to the nonlocality of the resulting fractional system, we construct a modified Adams–Bashforth–Moulton Predict–Evaluate–Correct–Evaluate (ABM–PECE) algorithm for its numerical solution. A large number of simulations are executed to explore the influence of the fractional order μ and different kernel functions ψ(t) on the displacement response, phase portraits and energy dissipation. </p> Results <p>It is found that decreasing μ induces a greater “suppressing” effect on vibrations, in particular by reducing limit-cycle oscillations and increasing their decay rate. Nonlinear kernel functions also provide additional versatility in tuning the effects, including through time-scaling and other energy transfer characteristics.</p> Conclusion <p>Overall, comparisons with the classical integer-order case establish the promise of the proposed fractional approach for improving passive vibration control in nonlinear oscillatory systems.</p>