A NOVEL VARIATIONAL APPROACH TO FRACTAL SWIFT–HOHENBERG MODEL ARISING IN FLUID DYNAMICS

Abstract

The problem of the fractal Swift–Hohenberg model (FSHM) with variable coefficient is considered in this work based on the fractal derivative. First, the fractal variational principle (FVP) of the FSHM with variable coefficient is successfully established by employing the fractal semi-inverse method (FSIM), which is very helpful to investigate the structure of the analytical solution. Second, the fractal two-scale variational method (FTSVM) is established by combining the FVP and fractal two-scale transform method (FTSTM). Finally, an example is presented to illustrate the proposed method which is efficient and accurate. The proposed fractal two-scale variational method sheds new light on the nonlinear fractal models.