In this paper, we implement the local fractional natural homotopy perturbation method (LFNHPM) to solve certain local fractional partial differential equations (LFPDEs) with fractal initial conditions occurring in physical sciences in a fractal domain. LFPDEs successfully exhibit the important properties of physical models occurring in a fractal medium. The working methodology depicts the feasibility and accuracy of the implemented approach for given LFPDEs. Moreover, the solutions for LFPDEs are obtained in a closed form and are in good agreement with the previously determined results. The numerical simulations are also investigated for each of the LFPDE on Cantor set. The implementation of the method in view of numerical simulations authenticates that the applied method is precise, and useful to investigate the solutions of partial differential equations with local fractional derivatives.