International Journal of Nonlinear Analysis and Applications

Lie symmetries, conservation laws, optimal system and power series solutions of (3+1)-dimensional fractional Zakharov-Kuznetsov equation

Document Type : Research Paper

Authors

1 School of Science, Wuhan University of Science and Technology, Wuhan 430081, Hubei, China

2 Hubei Province Key Laboratory of Systems Science in Metallurgical Process, Wuhan 430081, Hubei, China

Abstract

In this paper, the Lie symmetry analysis method is applied to the high dimensional fractional Zakharov-Kuznetsov equation. All Lie symmetries and the corresponding conserved vectors for the equation are obtained. The one-dimensional optimal system is utilized to reduce the aimed equation with Riemann-Liouville fractional derivative to a low-dimensional fractional partial differential equation with Erdelyi-Kober fractional derivative. Then the power series solution of the reduced equation is given. Moreover, some other low dimensional reduced fractional differential equations with Riemann-Liouville fractional derivatives are obtained and can be solved by different methods in the literatures herein.

Keywords

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International Journal of Nonlinear Analysis and Applications
Volume 16, Issue 3
March 2025
Pages 361-377
  • Receive Date: 10 December 2023
  • Revise Date: 13 January 2024
  • Accept Date: 15 January 2024