  This paper studies the properties of weak solutions to a class of space-time
fractional parabolic-elliptic Keller-Segel equations with logistic source terms
in $\mathbb{R}^{n}$, $n\geq 2$. The global existence and $L^{\infty}$-bound of
weak solutions are established. We mainly divide the damping coefficient into
two cases: (i) $b>1-\frac{\alpha}{n}$, for any initial value and birth rate;
(ii) $0<b\leq 1-\frac{\alpha}{n}$, for small initial value and small birth
rate. The existence result is obtained by verifying the existence of a solution
to the constructed regularization equation and incorporate the generalized
compactness criterion of time fractional partial differential equation. At the
same time, we get the $L^{\infty}$-bound of weak solutions by establishing the
fractional differential inequality and using the Moser iterative method.
Furthermore, we prove the uniqueness of weak solutions by using the
hyper-contractive estimates when the damping coefficient is strong. Finally, we
also propose a blow-up criterion for weak solutions, that is, if a weak
solution blows up in finite time, then for all $h>q$, the $L^{h}$-norms of the
weak solution blow up at the same time.
