Temporal anomalous diffusion and drift of particles in a comb backbone with fractional Cattaneo−Christov flux

Abstract

This paper investigates the temporal anomalous diffusion and drift of particles in a comb backbone. Fractional Cattaneo–Christov flux is introduced and the formulated governing equation has a Dirac delta function and mixed partial derivative which displays evolutional characteristics from parabolic (α → 0) to hyperbolic (α = 1). A solution is obtained numerically with the L1-scheme and the shifted Grünwald formula. Two completely opposite distributions are found: one is the monotonically decreasing convex distribution for the particle numbers and the other is the monotonically increasing concave distribution for the fractional order moments. The change rates of both the distributions decrease with the increase of time. Moreover, the influences of related parameters on the temporal evolution characteristics are discussed and analyzed in detail.