  The reductive perturbation method has been employed to derive the Korteweg-de
Vries (KdV) equation for small but finite amplitude electrostatic 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. Numerical studies have been
made using plasma parameters close to those values corresponding to the dayside
auroral zone. The effects of the time fractional parameter on the electrostatic
solitary structures are presented.
