Analysis of soliton profiles of the generalized P-type equation with conformable derivative via two distinct approaches

This work investigates the dynamics of a generalized (3+1)-dimensional Painleve integrable model with conformable derivative from various viewpoints, illustrating the evolution of nonlinear phe nomena across one temporal dimension and three spatial dimensions. The Kudryashov auxiliary equation approach and the Bernoulli's equation method are utilized to construct various traveling wave solutions in the form of hyperbolic and exponential functions. The new solutions are illus trated through contour, two-dimension, and three-dimension graphs, illustrating various dynamical structures with diverse parameter sets for a more thorough understanding of the physical principles. The findings reveal various soliton types, such as bell-shaped, bright, and dark solitons. The present solutions indicate that the current algorithm are highly effective and robust tools, making them suitable for solving a wide range of applied differential equations, including those with fractional and integer orders. Additionally, the study investigates the current conformable model of equations by investigating the influence of the conformable parameter and the time parameter on the present solutions