Interaction among lump, periodic, and kink solutions with dynamical analysis to the conformable time-fractional Phi-four equation

Abstract This study’s prime goal is to explore new and general analytic solutions to the conformal time-fractional Phi-four equation by utilizing the advanced exp ( − ϕ ( ξ ) ) -expansion approach with the conformable derivative principle’s help. This approach is essentially a modified particular case of the generalized form of exp ( − ϕ ( ξ ) ) -expansion method. Concerning hyperbolic and trigonometric function solutions, an enormous class of modern precise moving wave solutions is revealed. Some interaction solutions obtained, such as lump-periodic and lump-periodic-kink structure and periodic wave, are seen by showing their three-dimensional (3D) and two-dimensional (2D) combination plots with the aid of computational software Maple. We have portrayed the figures of the estimated solutions to understand the physical phenomena.