On Lie symmetry analysis and invariant subspace methods of coupled time fractional partial differential equations

R. Sahadevan; P. Prakash

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On Lie symmetry analysis and invariant subspace methods of coupled time fractional partial differential equations

机译：关于耦合时间分数偏微分方程的典型对称分析和不变子空间方法

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Highlights

?Considered five different coupled time fractional PDEs

?Derived Lie point symmetries, similarity reductions and exact solutions

?Derived different dimension of invariant subspaces

?Derived exact solutions for each of the invariant subspaces

?A comparison is made between Lie symmetry analysis and invariant subspace methods

Abstract

Lie symmetry analysis and invariant subspace methods of differential equations play an important role separately in the study of fractional partial differential equations. The former method helps to derive point symmetries, symmetry algebra and admissible exact solution, while the later one determines admissible invariant subspace as well as to derive exact solution of fractional partial differential equations. In this

机译：<！[cdata [ 亮点

？所考虑的五个不同耦合时间分数pdes

？派生的lie点对称，相似度缩减和精确解决方案

？派生不变子空间的不同维度

？为每个不变苏的精确解决方案bspace

？在Lie对称分析和不变子空间方法之间进行比较

抽象

LIE对称分析和差分方程的不变子空间方法在分数偏微分方程的研究中分开发挥重要作用。前一种方法有助于导出点对称，对称代数和可允许的精确解决方案，而后者确定可允许的不变子空间以及导出分数偏微分方程的精确解。在这方面

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来源
《Chaos, Solitons and Fractals: Applications in Science and Engineering: An Interdisciplinary Journal of Nonlinear Science》 |2017年第2017期|共14页
作者
R. Sahadevan; P. Prakash;
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作者单位

Ramanujan Institute for Advanced Study in Mathematics University of Madras;

Ramanujan Institute for Advanced Study in Mathematics University of Madras;

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原文格式 PDF
正文语种 eng
中图分类动力系统理论;
关键词
Lie group formalism; Invariant subspace method; System of time fractional PDEs; Exact solutions; Riemann-Liouville fractional derivative;

机译：Lie Group形式主义;不变子空间方法;时间分数PDES;精确的解决方案;Riemann-Liouville分数衍生物;

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专利

1. On Lie symmetry analysis and invariant subspace methods of coupled time fractional partial differential equations [J] . R. Sahadevan, P. Prakash Chaos, Solitons and Fractals: Applications in Science and Engineering: An Interdisciplinary Journal of Nonlinear Science . 2017,第期

机译：关于耦合时间分数偏微分方程的典型对称分析和不变子空间方法
2. On the conservation laws and invariant analysis for time-fractional coupled Fitzhugh-Nagumo equations using the Lie symmetry analysis [J] . Sahoo S., Ray S. Saha European Physical Journal Plus . 2019,第2期

机译：关于使用LIE对称分析的节约法和时间分数耦合Fitzhugh-Nagumo方程的不变分析
3. Lie symmetry analysis and conservation laws of certain time fractional partial differential equations [J] . R. Sahadevan, P. Prakash International journal of dynamical systems and differential equations . 2019,第1期

机译：某些时间分数阶偏微分方程的Lie对称性分析和守恒律
4. Construction of Exact Solutions for Fractional Order Differential Equations by Invariant Subspace Method [C] . R. K. Gazizov, A. A. Kasatkin Proceedings of the Fifth symposium on fractional differentiation and its applications . 2012

机译：不变子空间法构造分数阶微分方程的精确解
5. Krylov Subspace Spectral method with multigrid for a time-dependent, variable-coefficient partial differential equation [D] . Dozier, Haley Renee. 2016

机译：具有时变，变系数偏微分方程的多重网格Krylov子空间谱方法
6. Lie Symmetry Analysis and Explicit Solutions of the Time Fractional Fifth-Order KdV Equation [O] . Gang wei Wang, Tian zhou Xu, Tao Feng 2010

机译：时间分数阶五阶KdV方程的Lie对称性分析和显式解
7. The invariant subspace method for solving nonlinear fractional partial differential equations with generalized fractional derivatives [O] . Mohamed S. Abdel Latif, Abass H. Abdel Kader, Dumitru Baleanu 2020

机译：具有广义分数衍生物的非线性分数局部微分方程的不变子空间方法

On Lie symmetry analysis and invariant subspace methods of coupled time fractional partial differential equations

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