  The behaviour of solutions for a non-linear diffusion problem is studied. A
subordination principle is applied to obtain the variation of parameters
formula in the sense of Volterra equations, which leads to the integral
representation of a solution in terms of the fundamental solutions. This
representation, the so-called mild solution, is used to investigate some
properties about continuity and non-negativeness of solutions as well as to
prove a Fujita type blow-up result. Fujita's critical exponent is established
in terms of the parameters of the stable non-Gaussian process and a result for
global solutions is given.
