We first investigate the existence and nonexistence of weak solutions to time-fractional reaction diffusion problem \begin{document}$ \frac{\partial^\alpha u}{\partial t^\alpha}-\frac{\partial^2 x^2}+u\geq x^{-a}|u|^p, \, t>0, x\in (0, 1], \quad u(0, x) = u_0(x), 1] $\end{document} under inhomogeneous Dirichlet boundary condition u(t, 1) \delta, where $ u $, 0<\alpha<1 }{\partial t^\al...