The analytical analysis of nonlinear fractional-order dynamical models

The present research paper is related to the analytical solution of fractional-order nonlinear Swift-Hohenberg equations using an efficient technique. The presented model is related to the temperature and thermal convection of fluid dynamics which can also be used to explain the formation process in liquid surfaces bounded along a horizontally well-conducting boundary. In this work Laplace Adomian decomposition method is implemented because it require small volume of calculations. Unlike the variational iteration method and Homotopy pertubation method, the suggested technique required no variational parameter and having simple calculation of fractional derivative respectively. Numerical examples verify the validity of the suggested method. It is confirmed that the present method's solutions are in close contact with the solutions of other existing methods. It is also investigated through graphs and tables that the suggested method's solutions are almost identical with different analytical methods.

Automated summary

The research paper presents an efficient technique for solving fractional-order nonlinear Swift-Hohenberg equations related to fluid dynamics, showing that the Laplace Adomian decomposition method requires minimal calculations and produces solutions in close agreement with other existing methods. Numerical examples confirm the validity of the suggested method, demonstrating its almost identical solutions with various analytical methods through graphs and tables.