  In this paper we prove existence of entropy solutions to the time-fractional
porous medium type equation, $$\partial_t[k\ast(u-u_0)]-\operatorname{div}
(A(t,x)\nabla\varphi(u))=f\text{ in }Q_T=(0,T)\times\Omega,$$ with Dirichlet
boundary condition, initial condition $u(0,\cdot)=u_0$ in $\Omega$, and
$L^1$-data $f\in L^1((0,T)\times\Omega), u_0\in L^1(\Omega)$. To this end we
approximate the data by $L^\infty$-functions, use a known existence result of
weak solutions for these more regular data, and additionally a known
contraction principle for weak solutions, which can be adopted to the entropy
solutions.
