Abstract: We consider the precise description of the asymptotic behavior of the solution of fractional diffusion equations with initial data which belongs to a weighted `L^1` space.

Furthermore, we develop the arguments in Ishige-Kawakami (Math. Ann. 2012 and J. Evol. Equ. 2014) and establish a method to obtain the asymptotic expansions of the solutions to a nonlinear fractional diffusion equation with polynomial nonlinearity.

This talk is based on the joint work with Ishige (Tohoku University) and Michihisa (Hiroshima University).