Anomalous convection diffusion and wave coupling transport of cells on comb frame with fractional Cattaneo-Christov flux

作者：Liu, Lin; Zheng, Liancun^*; Liu, Fawang; Zhang, Xinxin

来源：Communications in Nonlinear Science & Numerical Simulation, 2016, 38: 45-58.

DOI：10.1016/j.cnsns.2016.02.009

• Cells transport
• Comb model
• Cattaneo-Christov flux
• Convection-diffusion

An improved Cattaneo-Christov flux model is proposed which can be used to capture the effects of the time and spatial relaxations, the time and spatial inhomogeneous diffusion and the spatial transition probability of cell transport in a highly non-homogeneous medium. Solutions are obtained by numerical discretization method where the time and spatial fractional derivative are discretized by the L1-approximation and shifted Grunwald definition, respectively. The solvability, stability and convergence of the numerical method for the special case of the Cattaneo-Christov equation are proved. Results indicate that the fractional convection diffusion-wave equation is an evolution equation which displays the coexisting characteristics of parabolicity and hyperbolicity. In other words, for alpha in (0, 1), the cells transport occupies the characteristics of coupling convection diffusion and wave spreading. Moreover, the effects of pertinent time parameter, time and spatial fractional derivative parameters, relaxation parameter, weight coefficient and the convection velocity on the anomalous transport of cells are shown graphically and analyzed in detail.

• 出版日期2016-9
• 单位北京科技大学