Numerical Investigation of Fractional-Order Swift-Hohenberg Equations via a Novel Transform

In this paper, the Elzaki transform decomposition method is implemented to solve the time-fractional Swift-Hohenberg equations. 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 the Caputo manner, the fractional derivative is described. The suggested method is easy to implement and needs a small number of calculations. The validity of the presented method is confirmed from the numerical examples. Illustrative figures are used to derive and verify the supporting analytical schemes for fractional-order of the proposed problems. It has been confirmed that the proposed method can be easily extended for the solution of other linear and non-linear fractional-order partial differential equations.

Automated summary

The Elzaki transform decomposition method was implemented to solve time-fractional Swift-Hohenberg equations in this paper, related to temperature and thermal convection in fluid dynamics. The Caputo manner was used to describe fractional derivatives. The method is easy to implement, requires few calculations, and has been validated through numerical examples. Illustrative figures were used to verify the analytical schemes for fractional-order problems proposed in the study.