Time-fractional Cahn–Allen and time-fractional Klein–Gordon equations: Lie symmetry analysis, explicit solutions and convergence analysis

2018 ◽  
Vol 493 ◽  
pp. 94-106 ◽  
Author(s):  
Mustafa Inc ◽  
Abdullahi Yusuf ◽  
Aliyu Isa Aliyu ◽  
Dumitru Baleanu
Keyword(s):  
Convergence Analysis ◽  
Lie Symmetry ◽  
Symmetry Analysis ◽  
Explicit Solutions ◽  
Lie Symmetry Analysis ◽  
Klein Gordon

scholarly journals Comments on the Paper “Lie Symmetry Analysis, Explicit Solutions, and Conservation Laws of a Spatially Two-Dimensional Burgers–Huxley Equation”

Symmetry ◽  
2020 ◽  
Vol 12 (6) ◽  
pp. 900
Author(s):  
Roman Cherniha
Keyword(s):  
Conservation Laws ◽  
Lie Symmetry ◽  
Symmetry Analysis ◽  
Explicit Solutions ◽  
Two Dimensional ◽  
Lie Symmetry Analysis ◽  
Huxley Equation

This comment is devoted to the paper “Lie Symmetry Analysis, Explicit Solutions, and Conservation Laws of a Spatially Two-Dimensional Burgers–Huxley Equation” (Symmery, 2020, vol.12, 170), in which several results are either incorrect, or incomplete, or misleading.

LIE SYMMETRY ANALYSIS TO THE WEAKLY COUPLED KAUP–KUPERSHMIDT EQUATION WITH TIME FRACTIONAL ORDER

Fractals ◽  
2019 ◽  
Vol 27 (04) ◽  
pp. 1950052 ◽  
Author(s):  
ZHENLI WANG ◽  
LIHUA ZHANG ◽  
CHUANZHONG LI
Keyword(s):  
Fractional Order ◽  
Group Analysis ◽  
Nonlinear Ordinary Differential Equation ◽  
Lie Symmetry ◽  
Symmetry Analysis ◽  
Explicit Solutions ◽  
Lie Group Analysis ◽  
Analysis Method ◽  
Lie Symmetry Analysis ◽  
Weakly Coupled

The aim of this paper is to apply the Lie group analysis method to the weakly coupled Kaup–Kupershmidt (KK) equation with time fractional order. We considered the symmetry analysis, explicit solutions to the weakly coupled time fractional KK (TF-KK) equation with Riemann–Liouville (RL) derivative. The weakly coupled TF-KK equation is reduced to a nonlinear ordinary differential equation (ODE) of fractional order. We solve the reduced fractional ODE using the sub-equation method.

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