The time-fractional generalized Z-K equation: Analysis of Lie group, similarity reduction, conservation laws, and explicit solutions

被引：1

作者：

AL-Denari, Rasha B. ^{[1
]}

Ahmed, Engy A. ^{[1
]}

Tharwat, Mohammed M. ^{[1
]}

机构：

[1] Beni Suef Univ, Fac Sci, Dept Math & Comp Sci, Bani Suwayf 62511, Egypt

来源：

MATHEMATICAL METHODS IN THE APPLIED SCIENCES | 2023年 / 46卷 / 04期

关键词：

conservation laws; explicit power series; fractional sub-equation method; lie group analysis; Riemann-Liouville derivatives; similarity reduction; time-fractional generalized Z-K equation; REAL-WORLD APPLICATIONS; ZAKHAROV-KUZNETSOV; CALCULUS;

D O I：

10.1002/mma.8773

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we consider the three-dimensional non-linear time-fractional generalized Zakharov-Kuznetsov (Z-K) equation that describes the dust-ion acoustic solitary waves in a magnetized dusty plasma. Based on the definition of the Riemann-Liouville (R-L) fractional derivatives, the analysis of the Lie group method can be applied to find the symmetries for the considered equation. After that, these symmetries enable us to transform the equation under study into a two-dimensional non-linear ordinary differential equation of fractional order in the sense of ErdLelyi-Kober (E-K) fractional operator. Also, we obtain a set of new analytical solutions for the time-fractional generalized Z-K equation via the power series and the fractional sub-equation methods. Furthermore, we compute the conservation laws for this equation with a detailed derivation based on the formal Lagrangian.

引用

页码：4475 / 4493

页数：19

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