Nonexistence of solutions to fractional parabolic problem with general nonlinearities

In this content, we investigate a class of fractional parabolic equation with general nonlinearities ∂ z(x,t)/∂ t-(Δ +λ )^β/2z(x,t)=a(x_1)f(z), where a and f are nondecreasing functions. We first prove that the monotone increasing property of the positive solutions in x_1 direction. Based on this, nonexistence of the solutions are obtained by using a contradiction argument. We believe these new ideas we introduced will be applied to solve more fractional parabolic problems.