  We theoretically investigate a practically realizable Floquet topological
superconductor model, based on a one-dimensional Rashba nanowire and proximity
induced $s$-wave superconductivity in the presence of a Zeeman field. The
driven system hosts regular $0$- and anomalous $\pi$-Majorana end modes~(MEMs).
By tuning the chemical potential and the frequency of the drive, we illustrate
the generation of multiple MEMs in our theoretical set up. We utilize the
chiral symmetry operator to topologically characterize these MEMs via a
dynamical winding number constructed out of the periodized evolution operator.
Interestingly, the robustness of the $0$- and $\pi$-MEMs is established in the
presence of on-site time-independent random disorder potential. We employ the
twisted boundary condition to define the dynamical topological invariant for
this translational-symmetry broken system. The interplay between the Floquet
driving and the weak disorder can stabilize the MEMs giving rise to a quantized
value of the dynamical winding number for a finite range of drive parameters.
This observation might be experimentally helpful in scrutinizing the
topological nature of the Floquet MEMs. We showcase another driving protocol
namely, a periodic kick in the chemical potential to study the generation of
Floquet MEMs in our setup. Our work paves a realistic way to engineer multiple
MEMs in a driven system.
