A novel method for numerical simulation of sand motion model in beach formation based on fractional Taylor-Jumarie series expansion and piecewise interpolation technique.

In this paper, for the first time, fractional Taylor–Jumarie series expansion is used to solve a glass of time-fractional delay partial differential equation by piecewise interpolation reproducing kernel method (RKM), this class of equations describe sand motion model in beach formation. The aim of this work is to obtain more accurate numerical solution by fractional Taylor–Jumarie series expansion and piecewise interpolation technique. Three numerical experiments are provided to show the advantage of this method, the results show the characteristics of sand motion. The research in this paper is the theoretical basis for further sand motion study.