Lie symmetry analysis, conservation laws and analytical solutions of the time-fractional thin-film equation

2018 ◽  
Vol 37 (5) ◽  
pp. 6270-6282 ◽  
Author(s):  
Xiu-Bin Wang ◽  
Shou-Fu Tian
Keyword(s):  
Thin Film ◽  
Conservation Laws ◽  
Analytical Solutions ◽  
Lie Symmetry ◽  
Symmetry Analysis ◽  
Lie Symmetry Analysis ◽  
Thin Film Equation

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.

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