Scaling behavior of the time-fractional equations for molecular-beam epitaxy growth: scaling analysis versus numerical stimulations

摘要

The scaling behavior of the time-fractional molecular-beam epitaxy (TFMBE) equations in1+1 dimensions is investigated by numerical simulations and scaling analysis, respectively. The growthequations studied include the time-fractional linear molecular-beam epitaxy (TFLMBE) and the time-fractional Lai-Das Sarma-Villain (TFLDV). Growth exponents are obtained using the two methods. Theanalytical results are consistent with the corresponding numerical solutions based on Caputo-type fractionalderivative.