Time fractional Cattaneo-Christov anomalous diffusion in comb frame with finite length of fingers

Fractional Cattaneo-Christov flux model is used in analyzing the anomalous diffusion in comb frame subject to finite length of fingers. Formulated governing equation contains Dirac delta function and mixed partial derivatives. Solutions are obtained by numerical discretization method where the time fractional derivative of order α in (0, 1] is approximated by L1-scheme. The correctness of numerical method is verified by introducing a source item to construct an exact solution. Results show that, when there exists relaxation, the particles distribution displays a parabolic feature with the spatial evolution at small times while a hyperbolic feature appears with a larger relaxation parameter at large times, the particles distribution and the total number of particles on x axis are oscillating with the temporal evolution. Moreover, the effects of involved parameters on dynamic characteristics are graphically analyzed and discussed in detail.