  In this Part II of D(11), we introduce new objects: super-$C^k$-schemes and
Azumaya super-$C^k$-manifolds with a fundamental module (or, synonymously,
matrix super-$C^k$-manifolds with a fundamental module), and extend the study
in D(11.1) ([L-Y3], arXiv:1406.0929 [math.DG]) to define the notion of
`differentiable maps from an Azumaya/matrix supermanifold with a fundamental
module to a real manifold or supermanifold'. This allows us to introduce the
notion of `fermionic D-branes' in two different styles, one parallels
Ramond-Neveu-Schwarz fermionic string and the other Green-Schwarz fermionic
string. A more detailed discussion on the Higgs mechanism on dynamical D-branes
in our setting, taking maps from the D-brane world-volume to the space-time in
question and/or sections of the Chan-Paton bundle on the D-brane world-volume
as Higgs fields, is also given for the first time in the D-project. Finally
note that mathematically string theory begins with the notion of a
differentiable map from a string world-sheet (a $2$-manifold) to a target
space-time (a real manifold). In comparison to this, D(11.1) and the current
D(11.2) together bring us to the same starting point for studying D-branes in
string theory as dynamical objects.
