Complete asymptotic expansion for integrals arising from one-dimensional diffusion with random traps

The solution of various diffusion problems, in both continuous and discrete systems, can be expressed in terms of a Laplace transform of the exponential function of a fractional power. In this Brief Report the need for a complete asymptotic analysis of these functions is discussed in the context of one-dimensional diffusion with random trapping sites and the necessary asymptotic analysis is carried out.