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This article is concerned with a semilinear time-fractional diffusionequation with a superlinear convex semilinear term in a bounded domain $\Omega$with the homogeneous Dirichlet, Neumann, Robin boundary conditions andnon-negative and not identically vanishing initial value. The order of thefractional derivative in time is between $1$ and $0$, and the elliptic part iswith time-independent coefficients. We prove  (i) The solution with any initial value blow-up if the eigenvalue $\lambda_1$of the elliptic operator with the minimum real part is non-positive.  (ii) Otherwise, the solution blows up if a weighted $L^1$-norm of initialvalue is greater than some critical value give by $\lambda_1$.  We provide upper estimates of the blow-up times. The key is a comparisonprinciple for time-fractional ordinary differential equations.

Blow-up for time-fractional diffusion equations with superlinear convex semilinear terms