Exploration of Soliton Solutions and Bifurcation Analysis in Fluid Dynamics Governed by M Fractional (3+1)‐Dimensional Generalized B‐Type Kadomtsev–Petviashvili ( gBKP ) Equation

ABSTRACT This study investigates the soliton solutions, stability, and chaotic characteristics of the M fractional (3+1)‐dimensional generalized B‐type Kadomtsev–Petviashvili (gBKP) equation, where a Galilean transformation is performed to get the related system of equations. Advanced mathematical and analytical techniques are utilized to explore the soliton solutions and bifurcation analysis in a fractional‐order nonlinear system, which helps to understand the functioning of complex systems. Perturbations are introduced to those systems to enable the observation of bifurcation analysis, including phase portraits. We also apply analytical technique the unified method to derive soliton solutions for the M‐fractional gBKP model. This work reveals various soliton solutions, including kink, anti‐kink, periodic waves, kinky periodic waves, and periodic lump waves. The solutions are graphically analyzed to explore their dynamic properties for fractional parameters. Moreover, we examine the suggested model's stability. We visualize the diverse range of soliton‐like solutions to demonstrate the significance of the findings and the effectiveness of the proposed methodology. These results enhance the understanding of soliton behaviors in M fractional gBKP equation and portray how effective the medium approach is for solving complicated nonlinear systems.