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.
Highlights
Lie symmetry analysis (LSA) is one of the most efficient method for investigating the exact solutions of nonlinear partial differential equations (NLPDEs) arising in mathematics, physics and many other fields of science and engineering
It is well known that there is no general method for solving NLPDEs, LSA is one of the more powerful method for reaching new exact and explicit solutions for NLPDEs [9, 11, 28, 31,32,33, 42, 44, 45, 55, 56, 60]
conservation laws (CLs) possess an important role in the analysis of NLPDEs from physical viewpoint [55]
Summary
LSA is one of the most efficient method for investigating the exact solutions of nonlinear partial differential equations (NLPDEs) arising in mathematics, physics and many other fields of science and engineering. We study Lie symmetry analysis, exact traveling wave solutions using fractional DξαG/G-expansion method and Ibragimov’s nonlocal CLs [30] of the time fractional mZK equation given by. When the order of the fractional derivative parameter can be controlled externally, the evolution of the soliton can be manifested artificially [4, 16, 17, 21, 48,49,50,51]. This important feature is being globally applied in several areas of physics and engineering. The mZK equation interprets an anisotropic two-dimensional generalization of the KdV equation and can be analysed in magnetized plasma for a tiny amplitude Alfven wave at a critical angle to the uninterrupted magnetic field [1, 5, 7, 8, 15, 34, 40, 41, 52, 58, 59, 64]
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