Analytical study of fractional solitons in three dimensional nonlinear evolution equation within fluid environments.

This study investigates a nonlinear (3+1)-dimensional evolution equation in the conformable fractional derivative (CFD) sense, which may be useful for comprehending how waves change in water bodies like seas and oceans. Certain intriguing non-linear molecular waves are linked to solitons and other modified waves that result from the velocity resonance condition. The characteristic lines of each wave component show that these waves have a set spacing throughout their propagation. We start by using the proposed model and the modified extended mapping technique. We also conduct an analysis of the various solutions, including bright, dark, and singular solitons; periodic wave solutions; exponential wave solutions; hyperbolic solutions; Jacobi elliptic function (JEF) solutions; Weierstrass elliptic doubly periodic solutions; and rational wave solutions. By clarifying how fractional-order dynamics modulate wave amplitude and dispersion features, the resulting solutions allow for a more realistic depiction of complicated fluid behaviors seen in empirical investigations of coastal and stratified oceanic settings. To provide them with a physical comprehension of the obtained solutions, some of the extracted solutions are illustrated visually. The obtained solutions reveal how fractional-order effects influence wave stability, energy transport, and interaction dynamics in fluid systems, offering practical insights for modeling coastal processes, pollutant dispersion, and wave-current interactions in real marine environments.