scholarly journals Lie symmetry analysis of conformable differential equations

2019 ◽  
Vol 4 (4) ◽  
pp. 1133-1144 ◽  
Author(s):  
Youness Chatibi ◽  
◽  
El Hassan El Kinani ◽  
Abdelaziz Ouhadan ◽  
Keyword(s):  
Differential Equations ◽  
Lie Symmetry ◽  
Symmetry Analysis ◽  
Lie Symmetry Analysis

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.

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.

scholarly journals ReLie: A Reduce Program for Lie Group Analysis of Differential Equations

Symmetry ◽  
2021 ◽  
Vol 13 (10) ◽  
pp. 1826
Author(s):  
Francesco Oliveri
Keyword(s):  
Differential Equations ◽  
Computer Algebra ◽  
Computer Algebra System ◽  
Source Code ◽  
Group Analysis ◽  
Lie Symmetry ◽  
Symmetry Analysis ◽  
Lie Group Analysis ◽  
Lie Symmetry Analysis ◽  
Source Program

Lie symmetry analysis provides a general theoretical framework for investigating ordinary and partial differential equations. The theory is completely algorithmic even if it usually involves lengthy computations. For this reason, along the years many computer algebra packages have been developed to automate the computation. In this paper, we describe the program ReLie, written in the Computer Algebra System Reduce, since 2008 an open source program for all platforms. ReLie is able to perform almost automatically the needed computations for Lie symmetry analysis of differential equations. Its source code is freely available too. The use of the program is illustrated by means of some examples; nevertheless, it is to be underlined that it proves effective also for more complex computations where one has to deal with very large expressions.

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