Simulating nonlinear wave dynamics requires methods that capture memory and nonlocal effects, making fractional methods especially effective and informative. In this work, we develop a fractional Korteweg-de Vries (KdV) system using the \(\phi \) -Caputo fractional derivative. The auxiliary function \(\phi (\eta )\) in this generalized derivative allows physically significant and controllable changes in the memory term which are not accessible to the classical fractional operators. We consider two semi-analytical methods the residual power series method and the new iterative method to find approximate solutions. The paper aims at comparing their behavior, particularly in the aspects of accuracy, convergence rate and the computation effort. Numerical tests indicate the response of both methods to variations in the fractional order and indicate differences in the response of the methods to dispersion and memory-driven deformation of the wave profile. A comparative study with the homotopy perturbation method also confirms that both the residual power series method and the new iterative method give much better accuracy, which results in smaller absolute errors in the entire range of fractional-order simulations. The results demonstrate that the residual power series method and the new iterative method differ significantly in their effectiveness when applied to nonlinear fractional KdV systems using the \(\phi \) -Caputo formulation, which provides a flexible method for modeling such waves.
