  We extend the notion of fragile topology to periodically-driven systems. We
demonstrate driving-induced fragile topology in two different models, namely,
the Floquet honeycomb model and the Floquet $\pi$-flux square-lattice model. In
both cases, we discover a rich phase diagram that includes Floquet fragile
topological phases protected by crystalline rotation or mirror symmetries,
Floquet Chern insulators, and trivial atomic phases, with distinct boundary
features. Remarkably, the transitions between different phases can be feasibly
achieved by simply tuning the driving amplitudes, which is a unique feature of
driving-enabled topological phenomena. Moreover, corner-localized fractional
charges are identified as a ``smoking-gun'' signal of fragile topology in our
systems. Our work paves the way for studying and realizing fragile topology in
Floquet systems.
