  We consider time fractional parabolic equations in both divergence and
non-divergence form when the leading coefficients $a^{ij}$ are measurable
functions of $(t,x_1)$ except for $a^{11}$ which is a measurable function of
either $t$ or $x_1$. We obtain the solvability in Sobolev spaces of the
equations in the whole space, on a half space, or on a partially bounded
domain. The proofs use a level set argument, a scaling argument, and embeddings
in fractional parabolic Sobolev spaces for which we give a direct and
elementary proof.
