  We consider a fractional diffusion equations of order $\alpha\in(0,1)$ whose
source term is singular in time: $(\partial_t^\alpha+A)u(x,t)=\mu(t)f(x)$,
$(x,t)\in\Omega\times(0,T)$, where $\mu$ belongs to a Sobolev space of negative
order. In inverse source problems of determining $f|_\Omega$ by the data
$u|_{\omega\times(0,T)}$ with a given subdomain $\omega\subset\Omega$ or
$\mu|_{(0,T)}$ by the data $u|_{\{x_0\}\times(0,T)}$ with a given point
$x_0\in\Omega$, we prove the uniqueness by reducing to the case $\mu\in
L^2(0,T)$. The key is a transformation of a solution to an initial-boundary
value problem with a regular function in time.
