  In this paper, we consider the Cauchy problem for the fractional Camassa-Holm
equation which models the propagation of small-but-finite amplitude long
unidirectional waves in a nonlocally and nonlinearly elastic medium. Using
Kato's semigroup approach for quasilinear evolution equations, we prove that
the Cauchy problem is locally well-posed for data in $H^{s}({\Bbb R})$,
$s>{\frac{5}{2}}$.
