Wave propagation analysis of the fractional generalized (3+1)-dimensional P-Type equation with local M-derivative

Abstract

This research article examines the influence of the local M-derivative on wave propagation in the fractional generalized (3+1)-dimensional P-type equation, a model with significant applications in plasma physics. The modified extended direct algebraic approach (MEDAA) is employed to derive a variety of exact solutions, including Jacobi elliptic function solutions, soliton solutions (bright, dark, and singular), Weierstrass elliptic function solutions, as well as hyperbolic, exponential, and singular periodic solutions. A comparative analysis with existing literature highlights the novelty and significance of the obtained wave solutions. Additionally, 3D, 2D, and contour plots are presented to visually illustrate the physical behavior of the extracted solutions. These solutions have a wide range of applications, including physics, engineering, plasma physics, ocean physics, nonlinear dynamics, and so on.