Lie symmetry analysis, exact solutions and conservation laws for the time fractional modified Zakharov–Kuznetsov equation
Articles
Dumitru Baleanu
Cankaya University, Turkey; Institute of Space Sciences, Romania
Mustafa Inc
Firat University, Turkey
Abdullahi Yusuf
Firat University, Turkey; Federal University Dutse, Nigeria
Aliyu Isa Isa Aliyu
Firat University, Turkey; Federal University Dutse, Nigeria
Published 2017-10-27
https://doi.org/10.15388/NA.2017.6.9
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Keywords

modified Zakharov–Kuznetsov equation
Lie symmetry
Riemann–Liouville fractional derivative
exact solutions
conservation laws

How to Cite

Baleanu, D. (2017) “Lie symmetry analysis, exact solutions and conservation laws for the time fractional modified Zakharov–Kuznetsov equation”, Nonlinear Analysis: Modelling and Control, 22(6), pp. 861–876. doi:10.15388/NA.2017.6.9.

Abstract

In this work, Lie symmetry analysis (LSA) for the time fractional modified Zakharov–Kuznetsov (mZK) equation with Riemann–Liouville (RL) derivative is analyzed. We transform the time fractional mZK equation to nonlinear ordinary differential equation (ODE) of fractional order using its point symmetries with a new dependent variable. In the reduced equation, the derivative is in Erdelyi–Kober (EK) sense. We obtained exact traveling wave solutions by using fractional DξαG/G-expansion method. Using Ibragimov's nonlocal conservation method to time fractional nonlinear partial differential equations (FNPDEs), we compute conservation laws (CLs) for the mZK equation.

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