Comparison of two reliable analytical methods based on the solutions of fractional coupled Klein–Gordon–Zakharov equations in plasma physics

In this paper, homotopy perturbation transform method and modified homotopy analysis method have been applied to obtain the approximate solutions of the time fractional coupled Klein–Gordon–Zakharov equations. We consider fractional coupled Klein–Gordon–Zakharov equation with appropriate initial values using homotopy perturbation transform method and modified homotopy analysis method. Here we obtain the solution of fractional coupled Klein–Gordon–Zakharov equation, which is obtained by replacing the time derivatives with a fractional derivatives of order $\alpha \in (1, 2], \beta \in (1, 2]$. Through error analysis and numerical simulation, we have compared approximate solutions obtained by two present methods homotopy perturbation transform method and modified homotopy analysis method. The fractional derivatives here are described in Caputo sense.