Dynamic scaling behaviors of linear fractal Langevin-type equation driven by nonconserved and conserved noise

In order to study the effects of the microscopic details of fractal substrates on the scaling behavior of the growth model, a generalized linear fractal Langevin-type equation, ∂h/∂t=(−1)m+1ν∇mzrwh (zrw is the dynamic exponent of random walk on substrates), driven by nonconserved and conserved noise is proposed and investigated theoretically employing scaling analysis. Corresponding dynamic scaling exponents are obtained.