scholarly journals Lie symmetry analysis and conservation laws for the time fractional simplified modified Kawahara equation

Open Physics ◽  
2018 ◽  
Vol 16 (1) ◽  
pp. 302-310 ◽  
Author(s):  
Dumitru Baleanu ◽  
Mustafa Inc ◽  
Abdullahi Yusuf ◽  
Aliyu Isa Aliyu
Keyword(s):  
Conservation Laws ◽  
Nonlinear Ordinary Differential Equation ◽  
Lie Symmetry ◽  
Symmetry Analysis ◽  
Lie Point Symmetries ◽  
Fractional Partial Differential Equations ◽  
Lie Symmetry Analysis ◽  
Kawahara Equation ◽  
Power Series Technique ◽  
Series Technique

AbstractIn this work, Lie symmetry analysis for the time fractional simplified modified Kawahara (SMK) equation with Riemann-Liouville (RL) derivative, is analyzed. We transform the time fractional SMK equation to nonlinear ordinary differential equation (ODE) of fractional order using its Lie point symmetries with a new dependent variable. In the reduced equation, the derivative is in the Erdelyi-Kober (EK) sense. We solve the reduced fractional ODE using a power series technique. Using Ibragimov’s nonlocal conservation method to time fractional partial differential equations, we compute conservation laws (Cls) for the time fractional SMK equation. Some figures of the obtained explicit solution are presented.

scholarly journals Conservation Laws and Exact Series Solution of Fractional-Order Hirota-Satsoma Coupled KdV system by Symmetry Analysis

2021 ◽  
Author(s):  
Hemant Gandhi ◽  
Amit Tomar ◽  
Dimple Singh
Keyword(s):  
Conservation Laws ◽  
Fractional Order ◽  
Lie Symmetry ◽  
Symmetry Analysis ◽  
Lie Symmetry Analysis ◽  
Infinitesimal Generators ◽  
Coupled Equations ◽  
Fractional Differential ◽  
Power Series Technique ◽  
Series Technique

In this work, we investigated the invariance analysis of fractional-order Hirota-Satsoma coupled Korteveg-de-Vries (HSC-KdV) system of equations based on Riemann-Liouville (RL) derivatives. The Lie Symmetry analysis is considered to obtain infinitesimal generators; we reduced the system of coupled equations into nonlinear fractional ordinary differential equations (FODEs) with the help of Erdelyi’s-Kober (EK) fractional differential and integral operators. The reduced system of FODEs solved by means of the power series technique with its convergence. The conservation laws of the system constructed by Noether’s theorem.

scholarly journals Symmetry Analysis and Conservation Laws of a Generalization of the Kelvin-Voigt Viscoelasticity Equation

Symmetry ◽  
2019 ◽  
Vol 11 (7) ◽  
pp. 840 ◽  
Author(s):  
Almudena P. Márquez ◽  
María S. Bruzón
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Partial Differential Equation ◽  
Conservation Laws ◽  
Mechanical Behaviour ◽  
Lie Symmetry ◽  
Symmetry Analysis ◽  
Lie Point Symmetries ◽  
Lie Symmetry Analysis ◽  
Partial Differential

In this paper, we study a generalization of the well-known Kelvin-Voigt viscoelasticity equation describing the mechanical behaviour of viscoelasticity. We perform a Lie symmetry analysis. Hence, we obtain the Lie point symmetries of the equation, allowing us to transform the partial differential equation into an ordinary differential equation by using the symmetry reductions. Furthermore, we determine the conservation laws of this equation by applying the multiplier method.

Lie symmetry analysis, conservation laws and some exact solutions of the time-fractional Buckmaster equation

2020 ◽  
Vol 17 (03) ◽  
pp. 2050040
Author(s):  
Mahdieh Yourdkhany ◽  
Mehdi Nadjafikhah ◽  
Megerdich Toomanian
Keyword(s):  
Power Series ◽  
Conservation Laws ◽  
Fractional Derivatives ◽  
Nonlinear Ordinary Differential Equation ◽  
Lie Symmetry ◽  
Symmetry Analysis ◽  
Lie Symmetry Analysis ◽  
Power Series Method ◽  
Power Series Solutions ◽  
Liouville Fractional Derivative

This paper systematically investigates the Lie symmetry analysis of the time-fractional Buckmaster equation in the sense of Riemann–Liouville fractional derivative. With the aid of infinitesimal symmetries, this equation is transformed into a nonlinear ordinary differential equation of fractional order (FODE), where the fractional derivatives are in Erdelyi–Kober sense. The reduced FODE is solved with the explicit power series method and some figures for the obtained power series solutions are also depicted. Finally, Ibragimov’s method and Noether’s theorem have been employed to conclude the conservation laws of this equation.

Symmetry analysis and conservation laws of the time fractional Kaup-Kupershmidt equation from capillary gravity waves

2018 ◽  
Vol 13 (2) ◽  
pp. 24
Author(s):  
Zhonglong Zhao ◽  
Bo Han
Keyword(s):  
Conservation Laws ◽  
Gravity Waves ◽  
Lie Symmetry ◽  
Symmetry Analysis ◽  
Lie Point Symmetries ◽  
Lie Symmetry Analysis ◽  
Similarity Reduction

The Lie symmetry analysis is employed to study the time fractional Kaup-Kupershmidt equation from capillary gravity waves. The Lie point symmetries and the similarity reduction of this equation are obtained. Then we construct the conservation laws by means of Ibragimov’s method.

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