الفهرس 
Introduction
Results and discussionOnly 14 pages are availabe for public view
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Abstract
The reductive perturbation method has been employed to derive the Korteweg-de Vries (KdV) equations, the modified KdV equation, the Burgers equation, and the KdV-Burgers equation. The Lagrangian of the time fractional form of these equations are used in similar form to the Lagrangian of the regular equations. The variation of the functional of this Lagrangian leads to the Euler-Lagrange equation that leads to the time fractional form for these equations. The Riemann-Liouville definition of the fractional derivative is used to describe the time fractional operator in the fractional form of these equations. The variational-iteration method given by He is used to solve the derived time fractional forms of these equations. Some different plasma physical systems have been taking as real physical applications, and studied using the time fractional KdV equation. The time fractional KdV equation is derived for small but finite amplitude electron-acoustic solitary waves in plasma of cold electron fluid with two different temperature ions. This system support two kinds of potential structure namely, compressive and rarefactive pulses. Depending on the sign of the coefficient of the nonlinear term ( ), compressive soliton exists if while rarefactive soliton exists if In order to describe the solitary waves at the critical hot density region, higher order nonlinearity must be considered (modified KdV equation). The effects of the time fractional parameter on the electrostatic solitary structures are presented. It is shown that the effect of time fractional parameter can be used to modify the amplitude of the electrostatic waves (viz. the amplitude, width and electric field) of the electron-acoustic solitary waves. The calculations show that the time fractional can be used to modulate the electrostatic potential wave instead of adding a higher order dissipation term to the KdV equation. The dust fluid dissipation can be caused by dust fluid viscosity, dust-dust collision, dust charge fluctuation, and Landau damping, with adding the nonlinearity and dispersion which would be described by using the Burgers’ equation or the KdV-Burgers equation. The time-fractional Burgers and KdV-Burgers’ equations for homogeneous unmagnetized plasma having electrons, singly charged ions, hot and cold dust species are derived. The effects of the different plasma parameters and the effect of the time-fractional order are presented.