Numerical investigation with stability analysis of time-fractional Korteweg-de Vries equations

In this paper, existing classical Korteweg-de Vries (KdV) equations are converted into the corresponding time-fractional KdV equations by using Caputo-Fabrizio fractional derivative and then solved with appropriate initial conditions by implementing semi-numerical technique, that is, Laplace transform together with an iterative scheme. The obtained solutions are novel, and previous literature lacks such derivations. The stability of implemented technique is analyzed by applying Banach contraction principle and S-stable mapping. Efficiency of Caputo-Fabrizio fractional derivative is exhibited through graphical illustrations, and fractional results are drafted in tabular form for specific values of fractional parameter to validate the numerical investigation.