On the approximate solution of nonlinear time-fractional KdV equation via modified homotopy analysis Laplace transform method

The approximate solution of the time-fractional KdV equation (KdV) by using modified homotopy analysis Laplace transform method, which is a combined form of the Laplace transform and homotopy analysis methods, is investigated for the first time in this article. Comparison of series solutions between under a rapid convergence and the optimal values of convergence parameter ħ is made. The results through the L₂ and L_∞ error norms are also analyzed. The validity, flexibility, and accuracy of the proposed method is conformed through the numerical computations as well as graphical presentations of the results.