(untitled) (Contemporary Mathematics, 2025)
This investigation studies the newly created (3+1)-D Kadomtsev-Petviashvili-Sawada-Kotera-Ramani equation with the effect of the conformable fractional derivative. The modified extended direct algebraic approach is used to investigate novel solitons and various other exact solutions. Furthermore, several kinds of analytical solutions are created, including bright, dark, and singular solitons. Additionally, singular periodic, hyperbolic solutions, Weierstrass elliptic doubly periodic solutions, and exponential solutions are derived. This study provides a framework for explaining various nonlinear phenomena that emerge in a variety of scientific fields, including fluid mechanics, ocean physics, and marine physics. Different types of acquired solutions are visually displayed to assist them with a physical understanding of the results in the sense of the conformable fractional derivative. Our findings shed light on the intricate dynamics of fluid waves and give vital new insights into the behavior of traveling waves and their many forms.