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

2017 ◽  
Vol 104 ◽  
pp. 107-120 ◽  
Author(s):  
R. Sahadevan ◽  
P. Prakash
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Invariant Subspace ◽  
Lie Symmetry ◽  
Symmetry Analysis ◽  
Fractional Partial Differential Equations ◽  
Subspace Methods ◽  
Lie Symmetry Analysis ◽  
Partial Differential

scholarly journals Lie symmetry analysis of some time fractional partial differential equations

2015 ◽  
Vol 38 ◽  
pp. 1560075 ◽  
Author(s):  
E. H. El Kinani ◽  
A. Ouhadan
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Exact Solutions ◽  
Lie Symmetry ◽  
Symmetry Analysis ◽  
Fractional Partial Differential Equations ◽  
Lie Symmetry Analysis ◽  
Partial Differential ◽  
Independent Variables ◽  
Symmetry Properties

This paper uses Lie symmetry analysis to reduce the number of independent variables of time fractional partial differential equations. Then symmetry properties have been employed to construct some exact solutions.

The Invariant Subspace Method for Solving Fractional Partial Differential Equations

2020 ◽  
pp. 267-282
Author(s):  
Mohamed Soror Abdel Latif ◽  
Abass Hassan Abdel Kader
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Invariant Subspace ◽  
Three Dimensional ◽  
Variable Coefficients ◽  
Subspace Method ◽  
Fractional Partial Differential Equations ◽  
Partial Differential ◽  
Balance Principle ◽  
New Exact Solutions

In this chapter, the authors discuss the effectiveness of the invariant subspace method (ISM) for solving fractional partial differential equations. For this purpose, they have chosen a nonlinear time fractional partial differential equation (PDE) with variable coefficients to be investigated through this method. One-, two-, and three-dimensional invariant subspace classifications have been performed for this equation. Some new exact solutions have been obtained using the ISM. Also, the authors give a comparison between this method and the homogeneous balance principle (HBP).

scholarly journals Invariant subspace method: A tool for solving fractional partial differential equations

2017 ◽  
Vol 20 (2) ◽  
Author(s):  
Sangita Choudhary ◽  
Varsha Daftardar-Gejji
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Invariant Subspace ◽  
Caputo Derivative ◽  
Linear Time ◽  
Subspace Method ◽  
Fractional Partial Differential Equations ◽  
Time And Space ◽  
Partial Differential ◽  
Non Linear

AbstractIn this paper invariant subspace method has been employed for solving linear and non-linear time and space fractional partial differential equations involving Caputo derivative. A variety of illustrative examples are solved to demonstrate the effectiveness and applicability of the method.

scholarly journals Lie Symmetry Analysis of C 1 m , a , b Partial Differential Equations

2021 ◽  
Vol 2021 ◽  
pp. 1-7
Author(s):  
Hengtai Wang ◽  
Aminu Ma’aruf Nass ◽  
Zhiwei Zou
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Conservation Laws ◽  
Symmetry Algebra ◽  
Lie Symmetry ◽  
Symmetry Analysis ◽  
Invariant Solutions ◽  
Lie Symmetry Analysis ◽  
Low Dimensions ◽  
Similarity Reductions

In this article, we discussed the Lie symmetry analysis of C 1 m , a , b fractional and integer order differential equations. The symmetry algebra of both differential equations is obtained and utilized to find the similarity reductions, invariant solutions, and conservation laws. In both cases, the symmetry algebra is of low dimensions.

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