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

•A generalized linear fractal Langevin-type equation driven by nonconserved and conserved noise is proposed.•The scaling behaviors of this equation are investigated theoretically by scaling analysis.•Corresponding dynamic scaling exponents are very consistent with the numerical results of simulation.

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∂h/∂t=(−1)m+1ν∇mzrwh (zrwzrw 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.