Variation of the Influence of Atangana-Conformable Time-Derivative on Various Physical Structures in the Fractional KP-BBM Model

The aim of this research is to explore the influence of fractional derivatives on solutions of various physical forms within a single mathematical model. By examining the Kadomtsev-Petviashvili-Benjamin-Bona-Mahony equation with the inclusion of temporal Atangana-conformable derivatives, and utilizing two effective methods, we observe distinct variations in the impact of the fractional derivative on altering the inherent physical properties of the proposed model. This research highlights an important function of the fractional derivative, indicating its role as a memory transmitter. This role illustrates how the physical characteristics inherent in the proposed application evolve as the value of the fractional derivative changes within the range of (0, 1) and nears that of the integer derivative. Finally, we provide illustrative 2D-plots to reinforce the findings of this study.