Moving-boundary problems for the time-fractional diffusion equation

Abstract

We consider a one-dimensional moving-boundary problem for thetime-fractional diffusion equation. The time-fractional derivative of order α ∈(0, 1) is taken in the sense of Caputo. We study the asymptotic behaivor, ast tends to infinity, of a general solution by using a fractional weak maximumprinciple. Also, we give some particular exact solutions in terms of Wright functions.