Lie Symmetry Analysis of Fractional Differential Equations

2020 ◽  
Author(s):  
Mir Sajjad Hashemi ◽  
Dumitru Baleanu
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
Lie Symmetry ◽  
Symmetry Analysis ◽  
Lie Symmetry Analysis ◽  
Fractional Differential

scholarly journals New Soliton Solutions of Fractional Jaulent-Miodek System with Symmetry Analysis

Symmetry ◽  
2020 ◽  
Vol 12 (6) ◽  
pp. 1001 ◽  
Author(s):  
Subhadarshan Sahoo ◽  
Santanu Saha Ray ◽  
Mohamed Aly Mohamed Abdou ◽  
Mustafa Inc ◽  
Yu-Ming Chu
Keyword(s):  
Conservation Laws ◽  
Fractional Differential Equations ◽  
Soliton Solutions ◽  
Logistic Function ◽  
Lie Symmetry ◽  
Symmetry Analysis ◽  
Analysis Method ◽  
Lie Symmetry Analysis ◽  
Fractional Differential ◽  
Physical Phenomena

New soliton solutions of fractional Jaulent-Miodek (JM) system are presented via symmetry analysis and fractional logistic function methods. Fractional Lie symmetry analysis is unified with symmetry analysis method. Conservation laws of the system are used to obtain new conserved vectors. Numerical simulations of the JM equations and efficiency of the methods are presented. These solutions might be imperative and significant for the explanation of some practical physical phenomena. The results show that present methods are powerful, competitive, reliable, and easy to implement for the nonlinear fractional differential equations.

scholarly journals Lie symmetry analysis for the solution of first-order linear and nonlinear fractional differential equations

2018 ◽  
Vol 7 (2) ◽  
pp. 37 ◽  
Author(s):  
Mousa Ilie ◽  
Jafar Biazar ◽  
Zainab Ayati
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
Lie Symmetry ◽  
Order Linear ◽  
Nonlinear Fractional Differential Equations ◽  
First Order ◽  
Fractional Equations ◽  
Fractional Differential ◽  
Linear And Nonlinear ◽  
Fractional Equation

Obtaining analytical or numerical solution of fractional differential equations is one of the troublesome and challenging issues among mathematicians and engineers, specifically in recent years. The purpose of this paper is to solve linear and nonlinear fractional differential equations such as first order linear fractional equation, Bernoulli, and Riccati fractional equations by using Lie Symmetry method, based on conformable fractional derivative. For each equation, some numerical examples are presented to illustrate the proposed approach.  

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.

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