Dynamical behavior of lump, breather and soliton solutions of time-fractional (3+1)D-YTSF equation with variable coefficients

The objective of this article is to investigate soliton, breather and lump solutions for the fractional (3+1)D–Yu–Toda–Sasa–Fukuyama (YTSF) equation with time-dependent variable coefficients, which is concerned with interfacial waves in a dual-layer liquid or elastic quasi-plane waves within a lattice. In particular case, YTSF equation reduces to the Kadomtsev–Petviashvili equation, which describes the long wave with small amplitude and slow dependence on the transverse coordinate in a single-layer shallow fluid or surface wave and the internal wave in the strait or channel of varying depth and width. Also, the YTSF equation reduces to Calogero–Bogoyavlenskii–Schiff equation, which describes the \((2+1)\) $(2+1)$ -dimensional interaction between a Riemann wave propagating along the z-axis and a long wave propagating along the x-axis. For the first time, the Hirota bilinear method is utilized in the context of a fractional differential equation with varying coefficients. To provide a detailed insight into the dynamic behavior of the wave profile, we explore various types of complex solutions such as multi-solitons, lump, and breather solutions. Using the multi-soliton solutions as a foundation, we derive breather wave, lump and hybrid solutions. Graphical discussion is conducted to explore the impact of time-dependent coefficients and fractional derivative on the solutions.