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More and more researches evidence that hemodynamic factors play an important role in the occurrence and development of cardiovascular diseases. In this paper, a new mathematical model has been proposed to describe rogue waves in arterial vessels. Based on two‐dimensional Navier–Stokes (NS) equation and continuity equation, vorticity equation satisfied by blood flow is given. Further, by employing multiscale analysis and perturbation expansion method, the (2+1)‐dimensional nonlinear Schrödinger (NLS) equation is derived to describe the envelope solitary waves propagation of blood vessels. Different from the previous model, the (2+1)‐dimensional NLS model takes into account the propagation of blood flow along the vessel axis and radius. In order to further study, the integer‐order model is generalized to the time‐fractional nonlinear Schrödinger (TF‐NLS) equation by use of the semi‐inverse method and Agrawal's method, and the conservation laws are also investigated. Moreover, the rogue wave solution of the fractional model which can directly describe the behavior of the rogue waves in arterial vessels is obtained. Rogue wave and fractional parameter effect on blood flow volume is analyzed and discussed, which can provide some help for the study of cardiovascular diseases. [ABSTRACT FROM AUTHOR]

Based on the investigation of (2+1)-dimensional ZK–mZK–BBM equation, it describes the gravity water waves in a long-wave regime. With the help of the semi-inverse method and the variational method, the time fractional ZK–mZK–BBM equation is derived in the sense of Riemann–Liouville fractional derivatives, which opens a new window for understanding the features of gravity water waves. Further, the symmetry of the (2+1)-dimensional time fractional ZK–mZK–BBM equation is studied by fractional order symmetry. Meanwhile, based on the new conservation theorem, the conserved laws of (2+1)-dimensional time fractional ZK–mZK–BBM equation are constructed. Finally, we show how to derive the solutions of the time fractional ZK–mZK–BBM equation by a bilinear method and the radial basis functions (RBFs) meshless approach. [ABSTRACT FROM AUTHOR]