General Transform Decomposition Method

In this research, we present a new numerical method for solving fractional partial differential equations. This new approach is based on the combination of the general transformation and decomposition method. The general transform is a new integral transform that generalizes most of the Laplace transforms. In this study, it is combined with the decomposition technique to solve the time-fractional Klein-Gordon equation (TFKGE). The solution is presented in the form of a comprehensive analytical series expansion. Additionally, we provide a thorough analysis of numerical examples that effectively highlight the robustness and efficacy of the proposed method.