Symmetries, Symmetry Reductions and Exact Solutions to the Generalized Nonlinear Fractional Wave Equations

被引：14

作者：

Liu, Han-Ze ^{[1
]}

Wang, Zeng-Gui ^{[1
]}

Xin, Xiang-Peng ^{[1
]}

Liu, Xi-Qiang ^{[1
]}

机构：

[1] Liaocheng Univ, Sch Math Sci, Liaocheng 252059, Peoples R China

来源：

COMMUNICATIONS IN THEORETICAL PHYSICS | 2018年 / 70卷 / 01期

基金：

中国国家自然科学基金;

关键词：

fractional differential equation; Riemann-Liouville derivative; Lie group classification; Erdelyi-Kober fractional operator; symmetry reduction; exact solution; GROUP CLASSIFICATION; HEAT-CONDUCTION; LIE GROUP; INVARIANCE;

D O I：

10.1088/0253-6102/70/1/14

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

In this paper, the Lie group classification method is performed on the fractional partial differential equation (FPDE), all of the point symmetries of the FPDEs are obtained. Then, the symmetry reductions and exact solutions to the fractional equations are presented, the compatibility of the symmetry analysis for the fractional and integer-order cases is verified. Especially, we reduce the FPDEs to the fractional ordinary differential equations (FODEs) in terms of the Erdelyi-Kober (E-K) fractional operator method, and extend the power series method for investigating exact solutions to the FPDEs.

引用

页码：14 / 18

页数：5

共 19 条

[11] The time fractional heat conduction equation in the general orthogonal curvilinear coordinate and the cylindrical coordinate systems [J].

Jiang, Xiaoyun ;

Xu, Mingyu .

PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS, 2010, 389 (17) :3368-3374

[12] Cauchy's integral formula via the modified Riemann-Liouville derivative for analytic functions of fractional order [J].

Jumarie, Guy .

APPLIED MATHEMATICS LETTERS, 2010, 23 (12) :1444-1450

[13] Complete Group Classification and Exact Solutions to the Generalized Short Pulse Equation [J].

Liu, H. ;

Li, J. ;

Liu, L. .

STUDIES IN APPLIED MATHEMATICS, 2012, 129 (01) :103-116

[14] Generalized symmetry classifications, integrable properties and exact solutions to the general nonlinear diffusion equations [J].

Liu, Hanze .

COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, 2016, 36 :21-28

[15] The unified group classification method for the generalized nonlinear wave equation and its partial difference schemes [J].

Liu, Hanze .

APPLIED MATHEMATICS AND COMPUTATION, 2015, 251 :203-210

[16] Complete Group Classifications and Symmetry Reductions of the Fractional Fifth-Order KdV Types of Equations [J].

Liu, Hanze .

STUDIES IN APPLIED MATHEMATICS, 2013, 131 (04) :317-330

[17]

Olver PJ., 2000, Applications of Lie Groups to Differential Equations

[18]

Podlubny I., 1974, FRACTIONAL DIFFERENT

[19] Exact solutions for fractional diffusion equation in a bounded domain with different boundary conditions [J].

Tomovski, Zivorad ;

Sandev, Trifce .

NONLINEAR DYNAMICS, 2013, 71 (04) :671-683

← 1 2 →