  We recently derived explicit solutions of the leading-order
Dokshitzer-Gribov-Lipatov-Altarelli-Parisi (DGLAP) equations for the $Q^2$
evolution of the singlet structure function $F_s(x,Q^2)$ and the gluon
distribution $G(x,Q^2)$ using very efficient Laplace transform techniques. We
apply our results here to a study of the HERA data on deep inelastic $ep$
scattering as recently combined by the H1 and ZEUS groups. We use initial
distributions $F_2^{\gamma p}(x,Q_0^2)$ and $G(x,Q_0^2)$ fixed by a global fit
to the HERA data. From $F_2^{\gamma p}(x,Q_0^2)$ we obtain the singlet quark
distribution $F_s(x,Q_0^2)$---using small non-singlet quark distributions taken
from either the CTEQ6L or the MSTW2008LO analyses---evolve to arbitrary $Q^2$,
and then convert the results to individual quark distributions. Finally, we
show directly from a study of systematic trends in a comparison of the evolved
$F_2^{\gamma p}(x,Q^2)$ with the HERA data, that the assumption of
leading-order DGLAP evolution is inconsistent with those data.
