In this short paper, we consider a sliding punch problem under recently proposed model of wear which is based on the Riemann-Liouville fractional integral relation between pressure and worn volume, and incorporates another additional effect pertinent to relaxation. A particular case of oscillatory (time-harmonic) load is studied. The time-dependent stationary state is identified in terms of eigenfunctions of an auxiliary integral operator. Convergence to this stationary state is quantified. Moreover, numerical simulations have been conducted in order to illustrate the obtained results and study qualitative dependence on two main model parameters.