Novel analysis of fractional regularized long-wave equation in plasma dynamics

Abstract In this study, we investigate the fractional regularized long-wave (FRLW) equation using the Aboodh transform iteration method (ATIM), a semi-analytical technique that effectively combines the Aboodh integral transform with iterative schemes to handle fractional differential equations. The FRLW equation, a nonlinear model arising in ion-acoustic wave propagation in plasma, is extended to the fractional domain to better capture the temporal nonlocal behavior. The proposed method provides approximate analytical solutions in a straightforward and computationally efficient manner. Graphical results are presented to demonstrate the impact of the fractional-order parameter on wave dynamics, including dispersion and stability. The results confirm that ATIM is a powerful and accurate approach for solving nonlinear fractional partial differential equations and enriches the analytical understanding of fractional plasma wave models.