Symmetry properties, conservation laws, reduction and numerical approximations of time-fractional cylindrical-Burgers equation

被引：17

作者：

Lashkarian, Elham ^{[1
]}

Hejazi, S. Reza ^{[1
]}

Habibi, Noora ^{[1
]}

Motamednezhad, Ahmad ^{[1
]}

机构：

[1] Shahrood Univ Technol, Fac Math Sci, Shahrood, Semnan, Iran

来源：

COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION | 2019年 / 67卷

关键词：

Symmetry analysis; Fractional derivatives; Chebyshev wavelets; Fractional conservation laws; Noether's theorem; DIFFERENTIAL-EQUATIONS; VARIATIONAL CALCULUS; EVOLUTION;

D O I：

10.1016/j.cnsns.2018.06.025

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper the Lie group analysis of the time-fractional cylindrical Burgers equation (time-FCB), which is a fundamental PDE occurring in various areas of applied mathematics, such as fluid mechanics, non-linear acoustics, gas dynamics, traffic flow and etc. is given. For this purpose the Riemann-Liouville derivative is used to implement the Lie algorithm for finding the symmetry operators. A reduced form of the equation is given by using the similarity variables obtained from a symmetry and Erdelyi-Kober operator. In the next step conservation laws are derived via a generalization of Noether's theorem. Finally the Chebyshev wavelets for time-fractional differential equations (FDEs) is applied for solving the considered equation. (C) 2018 Elsevier B.V. All rights reserved.

引用

页码：176 / 191

页数：16

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