The heat equation for the Dirichlet fractional Laplacian with negative   potentials: Existence and blow-up of nonnegative solutions
  We establish conditions ensuring either existence or blow-up of nonnegative solutions for the heat equation generated by the Dirichlet fractional Laplacian perturbed by negative potentials on bounded sets. The elaborated theory is supplied by some examples. 
Ali BenAmor and Tarek Kenzizi
math.FA