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

Symmetry

Abdullah M. Alsharif¹  Yasser S. Hamed¹  Adnan Khan²  Rasool Shah²  Ahmed M. Zidan³  Kamsing Nonlaopon⁴ 

[1] Department of Mathematics and Statistics, College of Science, Taif University, Taif 21944, Saudi Arabia;Department of Mathematics, Abdul Wali University Mardan, Mardan 23200, Pakistan;Department of Mathematics, College of Science, King Khalid University, Abha 61413, Saudi Arabia;Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen 40002, Thailand;

关键词: Elzaki transformation;    Adomian decomposition method;    time-fractional Swift–Hohenberg equation;    Caputo operator;   

DOI  :  10.3390/sym13071263

来源: DOAJ

【 摘 要 】

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.

【 授权许可】

Unknown