  This paper proposes fractional sliding control designs for
single-degree-of-freedom fractional oscillators respectively of the
Kelvin-Voigt type, the modified Kelvin-Voigt type and D\"{u}ffing type, whose
dynamical behaviors are described by second-order differential equations
involving fractional derivatives. Firstly, the differential equations of motion
are transformed into non-commensurate fractional state equations by introducing
state variables with physical significance. Secondly, fractional sliding
manifolds are constructed and stability of the corresponding sliding dynamics
is addressed via the infinite state approach and Lyapunov stability theory.
Thirdly, sliding control laws and adaptive sliding laws are designed for
fractional oscillators respectively in cases that the bound of the external
exciting force is known or unknown. Finally, numerical simulations are carried
out to validate the above control designs.
