The Large High Altitude Air Shower Observatory has reported the detection of cosmic-ray sources in Milky Way that can accelerate particles up to PeV (= 1015 eV) energies. These sources, so called ``PeVatrons'', are mostly unidentified. Several classes of sources, such as supernova remnants, pulsar wind nebula, or young stellar clusters can potentially be the counterparts of these PeVatrons. The aim of this work is to study a pulsar wind nebula interpretation of one of these PeVatrons, LHAASO J2226+6057, which has a relatively well covered multi-frequency spectrum. We have performed a leptonic, time-dependent modeling of the pulsar wind nebula (PWN) associated with PSR J2229+6114 considering a time-energy-dependent diffusion-loss equation. Injection, energy losses, as well as escape of particles were considered to balance the time-dependent lepton population. We have also included the dynamics of the PWN and the associated supernova remnant (SNR) and their interaction via the reverse shock to study the reverberation phase of the system. We have considered different values of braking index (n) and true age (tage) for the fitting of the multi-wavelength (MWL) spectral energy distribution (SED) of LHAASO J2226+6057. The best-fit PWN model parameters and their 1σ confidence intervals were evaluated. We have also demonstrated the impact of reverberation on the MWL SED with increasing time. Additionally, we have discussed the resultant large radius and low magnetic field associated with the PWN in question, as caveats for the possible physical connection of the pulsar as the origin of this high energy source.