Abstract
The task of our work is to consider the initial value problem based on the model of the generalized Kadomtsev-Petviashvili I equation and prove the local well-posedness in an anisotropic Gevrey spaces and then global well-posedness which improves the recent results on the well-posedness of this model in anisotropic Sobolev spaces [17]. Also, wide information about the regularity of the solution in the time variable is provided.