On the (2+1)-dimensional time-fractional Sakovich equation : Lie symmetry analysis, exact solutions, and conservation laws

Shi, Yapeng; Feng, Yuqiang; Yu, Jicheng

doi:10.47974/JIM-2325

Open Access Research Article

On the (2+1)-dimensional time-fractional Sakovich equation : Lie symmetry analysis, exact solutions, and conservation laws

Yapeng Shisypwust@163.comCollege of ScienceWuhan University of Science and TechnologyWuhan, Hubei, 430065, China0009-0004-2064-8127View full profile → , Yuqiang Fengyqfeng6@126.comAffiliation 1College of ScienceWuhan University of Science and TechnologyWuhan, Hubei, 430065, ChinaAffiliation 2Laboratory of Systems Science in Metallurgical ProcessHubei Province Key, Wuhan, Hubei, 430065, China0000-0002-1208-0509View full profile → , ^*Jicheng YuCorresponding authoryjicheng@126.comCollege of ScienceWuhan University of Science and TechnologyWuhan, Hubei, 430065, China0000-0001-6125-263XView full profile →

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pp. 1–18Online FirstMarch 2026DOI: 10.47974/JIM-2325XML

Received:: 01 Jan 2025
Published Online:: 28 Mar 2026
Article type:: Research Article
Language:: EN
Article no.:: JIM-2325
Pages:: 1–18

Abstract

Herein, we extend the framework of Lie symmetry group theory and conservation laws to analyze the (2+1)-dimensional time-fractional Sakovich equation ((2+1)D-TFSE). The distinctive feature of this equation, setting it apart from conventional time-fractional partial differential equations(TFPDEs), lies in its unique combination of the Riemann-Liouville time-fractional derivative and the integer-order derivative with respect to x. Therefore, we first transform the original equation into the form of a system of equations containing only fractional order derivatives in time, and then apply Lie symmetry methods to this system of equations. After finding these symmetries, the system of equations is transformed into a lower dimensional form and its power series solution is obtained by means of Erdélyi-Kober (E-K) fractional order differential operators. Finally, a new Noether’s theorem is used to establish a conservation law for the system of equations.

Keywords

Lie group method (2+1)D-TFSE Exact solutions Conservation laws

Subject Classifications

22E6022E7034A0834A25

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