An efficient semi-analytical techniques for the fractional-order system of Drinfeld-Sokolov-Wilson equation

Abstract

Abstract This study delves into the exploration and analysis of the fractional order Drinfeld-Sokolov-Wilson (FDSW) system within the framework of the Caputo operator. To address this complex system, two innovative methods, namely the Aboodh transform iteration method (ATIM) and the Aboodh residual power series method (ARPSM), are introduced and applied. These methods offer efficient computational tools to investigate the FDSW system, particularly in the fractional order context utilizing the Caputo operator. The ATIM and ARPSM are employed to solve and analyze the FDSW system, allowing for the derivation of solutions and insights into the system’s behavior and dynamics. The utilization of these novel methods showcases their efficacy in handling the intricate characteristics of the FDSW system under fractional differentiation, offering a deeper understanding of its mathematical properties and behaviors.