Fractional anomalous diffusion with Cattaneo-Christov flux effects in a comb-like structure

This paper investigates the fractional anomalous transport of particles in a comb-like structure. The higher spatial gradients are introduced in the constitutive relationship between the flux and the particles distribution and the effects of Cattaneo-Christov flux are taken into account. Formulated fractional governing equation displays a parabolic character for α in (0, 0.5) and the coexisting characteristics of the parabolic and hyperbolic for α→1 with relaxing parameter effect. When the relaxing parameter equals to zero, the equation reduces a parabolic equation which is derived from the classical Fick's first law of diffusion. Solutions are obtained numerically by using L1- and L2-approximations for fractional derivative. The effects of the involved parameters on particles distribution behavior are shown graphically and analyzed. Results indicate that the anomalous transport of particles possesses both diffusion and wave characteristics with the existence of relaxing time and for α → 1. Meanwhile, the formation of cusps has been discussed in detail.