Growing surfaces with anomalous diffusion: Results for the fractal Kardar-Parisi-Zhang equation

A model for a growing surface in the presence of anomalous diffusion, known as the fractal Kardar-Parisi-Zhang equation (FKPZ) was studied. The equation included a fractional Laplacian which accounted for the possibility that the cause of surface transport was a hopping mechanism of a Levy flight. To predict the critical exponents for the FKPZ model for any choice of the parameters and any spatial dimension, the self-consistent expansion (SCE) was used for the purpose.