Anomalous diffusion in comb model subject to a novel distributed order time fractional Cattaneo-Christov flux

Abstract The distributed order time fractional Cattaneo–Christov constitution relationship is firstly formulated to study the anomalous diffusion in comb model. The weight coefficients to govern the distributed order fractional diffusion are chosen as power-law forms. Solutions of the formulated governing equation containing the relaxation parameter and a spectrum of the fractional derivative are obtained numerically. By using mid-point quadrature rule, the distributed order item is transformed into multi-term fractional ones and the fractional derivatives are discretized by applying the L1 scheme. The effects of involved parameters on the spatial evolution and the power-law index evolution of particle distributions are discussed and the mass transfer mechanism is analysed by graphical illustrations.