  Given smooth manifolds $M_1,\ldots, M_n$ (which may have a boundary or
corners), a smooth manifold $N$ modeled on locally convex spaces and
$\alpha\in({\mathbb N}_0\cup\{\infty\})^n$, we consider the set
$C^\alpha(M_1\times\cdots\times M_n,N)$ of all mappings $f\colon
M_1\times\cdots\times M_n\to N$ which are $C^\alpha$ in the sense of Alzaareer.
Such mappings admit, simultaneously, continuous iterated directional
derivatives of orders $\leq \alpha_j$ in the $j$th variable for
$j\in\{1,\ldots, n\}$, in local charts. We show that
$C^\alpha(M_1\times\cdots\times M_n,N)$ admits a canonical smooth manifold
structure whenever each $M_j$ is compact and $N$ admits a local addition. The
case of non-compact domains is also considered.
