Abstract
The scaling behaviour of the time-fractional Kardar–Parisi–Zhang (TFKPZ) equation in (1 + 1) dimensions is investigated by scaling analysis and numerical simulations. The surface morphology and critical exponents with different fractional orders are obtained. The analytical results are consistent with the corresponding numerical solutions based on a Caputo-type fractional derivative. We find that, similar to the normal Kardar–Parisi–Zhang equation, anomalous behaviour does not appear in the TFKPZ model according to the scaling idea of local slope and numerical evidence. However, there exists significant finite-time effect of local scaling exponents in the TFKPZ system. Our results also imply that memory effects can affect the scaling behaviour of evolving fractional surface growth.
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