We investigate the well-posedness of a class of nonlinear dispersive waves on trees, in connection with the mathematical modeling of the human cardiovascular system. Specifically, we study the Benjamin-Bona-Mahony (BBM) equation, also known as the regularized long wave equation, posed on finite trees, together with standard junction and terminal boundary conditions. We prove that the Cauchy pro...

Abstract. The traditional wave equation models wave propagation in an ideal conducting medium. For characterizing the wave propagation in inhomogeneous media with frequency dependent power-law attenuation, the spacetime fractional wave equation appears; further incorporating the additive white Gaussian noise coming from many natural sources leads to the stochastic spacetime fractional wave equa...

This paper systematically investigates the Lie group analysis method of time-fractional regularized long-wave (RLW) equation with Riemann–Liouville fractional derivative. The vector fields and similarity reductions are obtained. It is shown that governing can be transformed into a ordinary differential new independent variable, where derivatives in Erdèlyi–Kober sense. Furthermore, explicit ana...