Fractional differentiation method: Application to the trapping reactions in the comb-like structures with relaxation

Abstract

The theory of subdiffusion and reactions occurring in confined domains such as comb structures has widespread applications in various fields of science. We study trapping diffusion-controlled reactions taking place in the backbone of a two-dimensional comb-like structure. A brief survey of previously published works on diffusion transport, both without and with inertial effects, is given. To take into account inertial effects, in this paper, we used the known Compte–Metzler analysis to choose an appropriate fractional diffusive Cattaneo system. By means of the chosen suitable fractional diffusive Cattaneo system, we derive the diffusion equation comprising a 1/2-order fractional time derivative as a damping term. With the help of the fractional differentiation method, we analytically evaluate the trapping reaction rate coefficient for short and long time regimes. Numerical calculations performed for the reaction rate coefficient showed a very good agreement with the obtained analytical expressions.