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The reductive perturbation method has been employed to derive the Korteweg-deVries (KdV) equation for small but finite amplitude electrostatic ion-acousticwaves in unmagnitized collisionless weakly relativistic warm plasma. TheLagrangian of the time fractional KdV equation is used in similar form to theLagrangian of the regular KdV equation. The variation of the functional of thisLagrangian leads to the Euler-Lagrange equation that leads to the timefractional KdV equation. The Riemann-Liouvulle definition of the fractionalderivative is used to describe the time fractional operator in the fractionalKdV equation. The variational-iteration method given by He is used to solve thederived time fractional KdV equation. The calculations of the solution withinitial condition A0*sech(cx)^2 are carried out. The result of the presentinvestigation may be applicable to some plasma environments, such asionosphere.

Ion-Acoustic Waves in Unmagnitized Collisionless Weakly Relativistic Plasma using Time-Fractional KdV Equation