Lie symmetry group, exact solutions and conservation laws for multi-term time fractional differential equations

被引：2

作者：

Yang, Miao ^{[1
]}

Wang, Lizhen ^{[1
]}

机构：

[1] Northwest Univ, Ctr Nonlinear Studies, Sch Math, Xian 710127, Peoples R China

来源：

AIMS MATHEMATICS | 2023年 / 8卷 / 12期

基金：

中国国家自然科学基金;

关键词：

Lie symmetry analysis; time-fractional BBMP equation; time-fractional Novikov equation; group-invariant solutions; conservation laws; EXPLICIT SOLUTIONS; POWER-LAW;

D O I：

10.3934/math.20231536

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, the time fractional Benjamin-Bona-Mahony-Peregrine (BBMP) equation and time-fractional Novikov equation with the Riemann-Liouville derivative are investigated through the use of Lie symmetry analysis and the new Noether's theorem. Then, we construct their group-invariant solutions by means of Lie symmetry reduction. In addition, the power-series solutions are also obtained with the help of the Erde ' lyi-Kober (E-K) fractional differential operator. Furthermore, the conservation laws for the time-fractional BBMP equation are established by utilizing the new Noether's theorem.

引用

页码：30038 / 30058

页数：21

共 40 条

[1] Numerical solution for generalized nonlinear fractional integro-differential equations with linear functional arguments using Chebyshev series [J].

Ali, Khalid K. ;

Abd El Salam, Mohamed A. ;

Mohamed, Emad M. H. ;

Samet, Bessem ;

Kumar, Sunil ;

Osman, M. S. .

ADVANCES IN DIFFERENCE EQUATIONS, 2020, 2020 (01)

[2]

[Anonymous], 2006, Exact solutions and invariant subspaces of nonlinear partial differential equations in mechanics and physics

[3] Lie symmetry analysis, exact solutions and conservation laws for the time fractional Caudrey-Dodd-Gibbon-Sawada-Kotera equation [J].

Baleanu, Dumitru ;

Inc, Mustafa ;

Yusuf, Abdullahi ;

Aliyu, Aliyu Isa .

COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, 2018, 59 :222-234

[4] Invariant analysis, exact solutions and conservation laws of (2+1)-dimensional time fractional Navier-Stokes equations [J].

Cheng, Xiaoyu ;

Wang, Lizhen .

PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, 2021, 477 (2250)

[5] Lie symmetry methods for multi-dimensional parabolic PDEs and diffusions [J].

Craddock, Mark ;

Lennox, Kelly A. .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2012, 252 (01) :56-90

[6] Symmetries and conservation laws of the Yao-Zeng two-component short-pulse equation [J].

Gao, Ben ;

Zhang, Yao .

BOUNDARY VALUE PROBLEMS, 2019, 2019 (1)

[7] Lie symmetry analysis of differential equations in finance [J].

Gazizov, RK ;

Ibragimov, NH .

NONLINEAR DYNAMICS, 1998, 17 (04) :387-407

[8] Variational iteration method - a kind of non-linear analytical technique: Some examples [J].

He, JH .

INTERNATIONAL JOURNAL OF NON-LINEAR MECHANICS, 1999, 34 (04) :699-708

[9] Lie symmetry analysis of the time fractional KdV-type equation [J].

Hu, Juan ;

Ye, Yujian ;

Shen, Shoufeng ;

Zhang, Jun .

APPLIED MATHEMATICS AND COMPUTATION, 2014, 233 :439-444

[10] Symmetries and exact solutions of the time fractional Harry-Dym equation with Riemann-Liouville derivative [J].

Huang, Qing ;

Zhdanov, Renat .

PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS, 2014, 409 :110-118

← 1 2 3 4 →