Time fractional Biswas–Milovic equation: Group analysis, soliton solutions, conservation laws and residual power series solution

Optik ◽  
2019 ◽  
Vol 183 ◽  
pp. 1085-1098 ◽  
Author(s):  
Baljinder Kour ◽  
Sachin Kumar
Keyword(s):  
Power Series ◽  
Conservation Laws ◽  
Series Solution ◽  
Group Analysis ◽  
Soliton Solutions ◽  
Power Series Solution ◽  
Residual Power Series ◽  
Equation Group ◽  
Residual Power

Time Fractional Third-Order Evolution Equation: Symmetry Analysis, Explicit Solutions, and Conservation Laws

2017 ◽  
Vol 13 (2) ◽  
Author(s):  
Dumitru Baleanu ◽  
Mustafa Inc ◽  
Abdullahi Yusuf ◽  
Aliyu Isa Aliyu
Keyword(s):  
Power Series ◽  
Conservation Laws ◽  
Series Solution ◽  
Three Dimensional ◽  
Nonlinear Ordinary Differential Equation ◽  
Symmetry Analysis ◽  
Power Series Solution ◽  
Lie Symmetry Analysis ◽  
Third Order ◽  
Contour Plots

In this work, Lie symmetry analysis for the time fractional third-order evolution (TOE) equation with Riemann–Liouville (RL) derivative is analyzed. We transform the time fractional TOE 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 Erdelyi–Kober (EK) sense. We obtain a kind of an explicit power series solution for the governing equation based on the power series theory. Using Ibragimov's nonlocal conservation method to time fractional partial differential equations (FPDEs), we compute conservation laws (CLs) for the TOE equation. Two dimensional (2D), three-dimensional (3D), and contour plots for the explicit power series solution are presented.

Lie Symmetries and Conservation Laws of the Generalised Foam-Drainage Equation

2017 ◽  
Vol 72 (3) ◽  
pp. 261-267 ◽  
Author(s):  
Zhi-Yong Zhang ◽  
Kai-Hua Ma
Keyword(s):  
Power Series ◽  
Conservation Laws ◽  
Series Solution ◽  
Power Series Solution ◽  
One Dimensional ◽  
Symmetry Classification ◽  
Symmetry Operators ◽  
Foam Drainage Equation ◽  
Foam Drainage

AbstractWe perform a complete Lie point symmetry classification of the generalised foam-drainage equation and then construct an optimal system of one-dimensional subalgebra of the admitted symmetry operators and use them to reduce the equations under study. A power series solution of the reduced equation is constructed. Moreover, we find all multipliers of the equations and apply them to construct conservation laws.

Optimal algebra and power series solution of fractional Black-Scholes pricing model

2021 ◽  
Vol 25 (8) ◽  
pp. 6075-6082
Author(s):  
Hemanta Mandal ◽  
B. Bira ◽  
D. Zeidan
Keyword(s):  
Power Series ◽  
Series Solution ◽  
Power Series Solution ◽  
Pricing Model ◽  
Black Scholes
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