Numerical Simulation of a Space-Fractional Molecular Beam Epitaxy Model without Slope Selection

In this paper, we introduce a space-fractional version of the molecular beam epitaxy (MBE) model without slope selection to describe super-diffusion in model. Compared classical MBE equation, spatial discretization is an important issue equation because nonlocal nature fractional operator. To approximate operator, employ Fourier spectral method, which gives full diagonal representation operator and achieves convergence regardless power. And, combine with method directly, present linear, energy stable, second-order method. Then, it possible simulate dynamics efficiently accurately. By using numerical investigate effect power equation.