Extracting explicit coefficient formulas: A robust approach to the laplace residual power series method

This work presents a novel advancement to the Laplace Residual Power Series Method (LRPSM) for solving fractional differential equations by specifically utilizing the Caputo fractional derivative. The conventional LRPSM relies on iterative calculations of the residual function to determine the series coefficients. We address this limitation by deriving a direct formula that yields all coefficients at once. This innovation significantly streamlines the computational process compared to the traditional LRPSM, leading to a more efficient method.