Propagation of shock wave of the time fractional Gardner Burger equation
in a multicomponent plasma using novel analytical method
Abstract
The time-fractional Gardner Burger (TFGB) equation is an efficient model
for studying nonlinear fluctuations of different types of wave profiles,
such as the gravity solitary waves in the ocean, ion-acoustic wave (IAW)
in a plasma environment, etc. Here, to build an example of the existence
of the classical Gardner Burger (GB) equation, a multi-component plasma
environment is considered and a classical GB equation is derived by
employing reductive perturbation technique (RPT) from the basic
governing equation. Further, the classical GB equation is converted into
the TFGB equation by applying Agrawal’s approach, where the Riesz
fractional derivative is adopted on the time-fractional term. A new
approach using the improved Bernoulli sub-equation function method
(IBSEFM) is carried out to solve the TFGB equation. Finally, some $2D$
and $3D$ graphs are plotted through which the physical structures of
the solution are explored and the effect of the Burgers term and
fractional order of the equation are determined.
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