Quenching phenomenon of a time-fractional diffusion equation with singular source term

In this paper, a time-fractional diffusion equation with singular source term is considered. The Caputo fractional derivative with order 0 < alpha <= 1 is applied to the temporal variable. Under specific initial and boundary conditions, we find that the time-fractional diffusion equation presents quenching solution that is not globally well-defined as time goes to infinity. The quenching time is estimated by using the eigenfunction of linear fractional diffusion equation. Moreover, by implementing a finite difference scheme, we give some numerical simulations to demonstrate the theoretical analysis. Copyright (c) 2017 John Wiley & Sons, Ltd.