Dynamics of generalized time-fractional viscous-capillarity compressible fluid model

This analysis examines the time-fractional mixed hyperbolic-elliptic p-system of conservation laws by applying the new extended direct algebraic method. The p-system with generalized cubic van der Waals flux, and potential applications in the field of compressible isothermal viscosity-capillarity fluids, is investigated. In particular, this issue describes the longitudinal isothermal motion in elastic bars or fluids. A diverse periodic, kink, and singular soliton structures are extracted. The 3D dynamical behaviors and corresponding contour profiles of some obtained solitons are displayed. The fractional effects in the sense of Beta, M-truncated, and modified Riemann–Liouville, are discussed and illustrated. The method shows the straightforward, reliability, and efficiency for solving complex physical phenomena that is modeled by nonlinear partial differential equations.