Efficient Conformable Laplace-Adomian Decomposition Method for Solving Nonlinear Fractional Partial Differential Equation Systems

This study introduces an innovative numerical technique, the Conformable Laplace-Adomian Decomposition Method (CLDM), to address challenges in solving nonlinear fractional partial differential equation systems (FPDEs), where traditional methods like finite difference and Adomian Decomposition Method (ADM) struggle due to numerical instability and inefficiency. CLDM synergizes the advantages of the conformable fractional derivative—which offers flexible algebraic rules (e.g., product and chain rules)—with the Laplace-Adomian decomposition framework, yielding accurate, stable solutions while reducing computational costs. The method’s efficacy was validated through applications in fluid mechanics and heat transfer, demonstrating superior accuracy and stability compared to Caputo-based, HPM, ADTM, and LRSPM approaches. This research contributes a novel methodology for handling complex fractional systems, a practical framework for scientific applications, and comparative insights into numerical method performance, paving the way for enhanced modeling of memorydriven phenomena in applied sciences and engineering.