<p>This work presents the application of the Laplace Homotopy Analysis Method (LHAM) to a time - fractional two - dimensional groundwater flow equation involving both Caputo and Caputo - Fabrizio derivatives. The fractional framework extends the classical model to incorporate memory and non-local transport effects in subsurface hydrology. Closed-form series solutions are constructed in the Laplace domain and analytically inverted to the time domain. The method guarantees consistency with the classical model as the fractional order approaches unity. Analytical results supported by convergence and stability analysis demonstrate the mathematical reliability of LHAM for both fractional operators. Furthermore, the distinct kernel structures of the Caputo and Caputo - Fabrizio derivatives are shown to influence the solution behavior, with observable differences in the evolution of hydraulic head profiles. The study provides a unified framework for comparing fractional models and establishes LHAM as a robust tool for analyzing complex groundwater flow governed by non-integer - order dynamics.</p>