A fractal langevin equation describing the kinetic roughening growth on fractal lattices

A fractal Langevin equation ( is the random walk exponent on the lattice) is proposed to describe the kinetic roughening growth on fractal substrates. The scaling relation can be obtained. Kinetic Monte Carlo simulations are carried out for Restricted Solid-on-solid model and Etching model growing on various fractal substrates, and the results prove this scaling relation.