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)β2z(x,t)=a(x1)f(z),\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{aligned} \frac{\partial z(x,t)}{\partial t}-(\Delta +\lambda )^{\frac{\beta }{2}}z(x,t)=a(x_{1})f(z), \end{aligned}$$\end{document}where a and f are nondecreasing functions. We first prove that the monotone increasing property of the positive solutions in x1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$x_{1}$$\end{document} 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.