Fractional differentiation method: Some applications to the theory of subdiffusion-controlled reactions

The fractional differentiation method's broad possibilities are demonstrated with rather simple but important examples of the anomalous diffusion trapping problems. In particular we evaluate the reaction rate coefficients for the subdiffusion-controlled reactions and for reactions describing by a diffusion equation with a half-order time derivative as a damping term. The distinctive feature of this aproach is that the reaction rate coefficient may be obtained by means of some factorization procedure immediately, without a preliminary solution to the corresponding initial boundary value diffusion problem. The explanations given in the paper are detailed enough to provide the mathematical background for the fractional differentiation method needed to apply it to a wide range of reaction-diffusion problems with time-fractional derivatives in the Riemann-Liouville sense.