Asymptotic Green's functions for time-fractional diffusion equation and their application for anomalous diffusion problem

Asymptotic Green's functions for short and long times for time-fractional diffusion equation, derived by simple and heuristic method, are provided in case if fractional derivative is presented in Caputo sense. The applicability of the asymptotic Green's functions for solving the anomalous diffusion problem on a semi-infinite rod is demonstrated. The initial value problem for longtime solution of the time-fractional diffusion equation by Green's function approach is resolved.