Scaling Behavior of Fractional Growth Processes

An exact solution is introduced for one dimensional space-fractional Edwards-Wilkinson equation. It is shown that the roughness obeys the Family-Viscek dynamic scaling form and the scaling exponents is derived. It is seen that the scaling exponents are different from those coming from ordinary Edwards-Wilkinson equation and depend on the fractional order. Scaling exponents in the presence of correlated noise is also obtained.