A Novel Laplace-Based Decomposition Technique for Fractional Navier–Stokes Systems with Memory Effects

This study presents a novel enhancement to the classical Laplace Transform Adomian Decomposition Method (LT-ADM) for the numerical solution of two-dimensional time-fractional Navier--Stokes equations involving the Atangana--Baleanu--Caputo (ABC) derivative. The proposed Modified LT-ADM (MLT-ADM) integrates an optimized, problem-adapted initial approximation obtained via a least-squares residual minimization framework. This modification enables the method to achieve high-accuracy solutions with a single iteration, markedly reducing computational overhead compared to its classical counterpart. Analytical investigations on and stability confirm the theoretical soundness of the proposed formulation, particularly in regimes dominated by strong memory and nonlocal effects. Numerical results further demonstrate the method’s capacity to deliver error reductions of several orders of magnitude while preserving physical fidelity across a wide spectrum of fractional orders. The synergy between the non-singular ABC operator and the optimized decomposition structure positions MLT-ADM as a robust, accurate, and scalable tool for simulating complex fractional fluid dynamics, with promising extensibility to higher-dimensional, variable-order, and coupled multiphysics systems.