Generalized KdV equation involving Riesz time-fractional derivatives: constructing and solution utilizing variational methods

Abstract

In this work, the time-fractional generalized Korteweg de Vries (TFGKdV) is derived by utilizing the method of a semi-inverse and the variational principles. Based on the initial condition relying on the dispersion and nonlinear coefficients, we can apply the He's variational iteration to construct an approximated solution for the TFGKdV equation. Finally, we study the impact of the fractional derivatives on the propagation and the structure of the solitary waves obtained from the solution of TFGKdV equation.