  The reductive perturbation method has been employed to derive the Korteweg-de
Vries (KdV) equation for small but finite amplitude electron-acoustic waves.
The Lagrangian of the time fractional KdV equation is used in similar form to
the Lagrangian of the regular KdV equation. The variation of the functional of
this Lagrangian leads to the Euler-Lagrange equation that leads to the time
fractional KdV equation. The Riemann-Liouvulle definition of the fractional
derivative is used to describe the time fractional operator in the fractional
KdV equation. The variational-iteration method given by He is used to solve the
derived time fractional KdV equation. The calculations of the solution with
initial condition A0*sech(cx)^2 are carried out. The result of the present
investigation may be applicable to some plasma environments, such as the
Earth's magnetotail region.
