A study on analytical solutions of one of the important shallow water wave equations and its stability analysis

The present research uses the modified w g -expansion technique to give analytical solutions for the nonlinear time fractional integro-differential Kadomtsev-Petviashvili (KP) hierarchy equation with beta fractional derivative. The modified w g -expansion technique is an important method for finding analytical solutions to nonlinear equations. The suggested approach produces three sorts of solutions: trigonometric, hyperbolic, and rational. These answers have been discovered with the aid of a software tool. Additionally, stability analysis of observed governing model solutions is used to validate scientific calculations. Furthermore, the 3-dimensional, contour, and 2-dimensional images are provided for a better understanding of the behavior of the solutions.