Nonexistence results for a fractional problem arising in thermal diffusion in fractal media

We consider the Cauchy problem for the fractional differential equationD1+αu+Dβu=Δu+h(t,x)upwith given initial data and where p > 1, −1 < α < 1, 0 < β < 2 and β < 1 + α. Nonexistence results and necessary conditions for global existence are established by means of the test-function method. These results improve and extend previous works.