A New Extension of Optimal Auxiliary Function Method to Fractional Non-Linear Coupled ITO System and Time Fractional Non-Linear KDV System

In this article, we investigate the utilization of Riemann–Liouville’s fractional integral and Caputo derivative in application Optimal Auxiliary Function Method (OAFM). The extended OAFM is employed to analyze non-linear coupled ITO systems KDV systems, which feature equations a order time. We compare results obtained for system with those derived from Homotopy Perturbation (HPM) New Iterative (NIM), Laplace Adomian Decomposition (LADM). demonstrates remarkable convergence single iteration, rendering it highly effective. contrast other existing analytical approaches, emerges as dependable efficient methodology, delivering high-precision solutions intricate problems while saving both computational resources Our indicate superior accuracy comparison HPM, NIM, LADM. Additionally, enhance through introduction supplementary auxiliary functions.