Quenching phenomenon in a fractional diffusion equation and its numerical simulation

In this paper, we introduced a fractional diffusion equation with degenerate source term. The fractional derivative, acting on the spatial variable, contains left-sided Caputo derivative and right-sided Riemann-Liouville derivative simultaneously. Due to the symmetry property of such fractional derivative pattern, the existence of quenching phenomenon is verified and the quenching time is estimated under certain settings of parameters. An numerical example is carried out by using a finite-difference scheme with uniform and non-unique mesh, which demonstrates the theoretical analysis of this model and presents several significant relation between order of derivatives and size of spatial domain.