A robust numerical framework for nonlinear Kuramoto-Sivashinsky problems with Caputo fractional derivatives

This study presents the Elzaki transform homotopy perturbation method ([Formula: see text]T-HPM) for deriving approximate solutions to nonlinear Kuramoto-Sivashinsky (K-S) problems with Caputo fractional derivatives. The proposed approach is free from discretization and linearization and does not require small perturbation parameters during the solution process. We employ the Elzaki transform ([Formula: see text]T) to transform the fractional derivative into an algebraic form, and then an embedding parameter is introduced through the homotopy perturbation method (HPM) to construct an iterative series of the resulting nonlinear relation. We provide two numerical examples and some graphical illustrations to validate the accuracy of convergent series with the actual solutions. The results showcase that the proposed approach yields high accuracy with a reduced number of expansion terms for fractional-order models.