  A (projective, geometrically irreducible, non-singular) curve $\mathcal{X}$
defined over a finite field $\mathbb{F}_{q^2}$ is maximal if the number
$N_{q^2}$ of its $\mathbb{F}_{q^2}$-rational points attains the Hasse-Weil
upper bound, that is $N_{q^2}=q^2+2\mathfrak{g}q+1$ where $\mathfrak{g}$ is the
genus of $\mathcal{X}$. An important question, also motivated by applications
to algebraic-geometry codes, is to find explicit equations for maximal curves.
For a few curves which are Galois covered of the Hermitian curve, this has been
done so far ad hoc, in particular in the cases where the Galois group has prime
order. In this paper we obtain explicit equations of all Galois covers of the
Hermitian curve with Galois group of order $p^2$ where $p$ is the
characteristic of $\mathbb{F}_{q^2}$. Doing so we also determine the
$\mathbb{F}_{q^2}$-isomorphism classes of such curves and describe their full
$\mathbb{F}_{q^2}$-automorphism groups.
