Title: Group classification, exact solutions and conservation laws of (2 + 1)-dimensional time fractional Konopelchenko-Dubrovsky equations

Authors: Jicheng Yu; Yuqiang Feng

Addresses: School of Science, Wuhan University of Science and Technology, Wuhan 430081, Hubei, China ' School of Science, Wuhan University of Science and Technology, Wuhan 430081, Hubei, China

Abstract: In this paper, Lie symmetry analysis method is applied to the (2 + 1)-dimensional time fractional Konopelchenko-Dubrovsky equations, which is an important model in physics. We obtained and classified all the Lie symmetries admitted by the equations according to the coefficients. Then we used the obtained group classification to reduce the (2 + 1)-dimensional fractional partial differential equations with Riemann-Liouville fractional derivative to some (1 + 1)-dimensional fractional partial differential equations with Erédlyi-Kober fractional derivative, thereby getting some exact solutions of the reduced equations. In addition, the new conservation theorem and the generalisation of Noether operators are developed to construct the conservation laws for the equations studied.

Keywords: Lie symmetry analysis; Riemann-Liouville fractional derivative; fractional modified Konopelchenko-Dubrovsky equations; Erdélyi-Kober fractional derivative; conservation laws.

DOI: 10.1504/IJDSDE.2024.145815

International Journal of Dynamical Systems and Differential Equations, 2024 Vol.13 No.6, pp.513 - 532

Received: 17 Jan 2024
Accepted: 25 Sep 2024
Published online: 25 Apr 2025 *

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