  We solve the Cauchy problem for the Schr\"odinger equation corresponding to
the family of Hamiltonians $H_{\gamma(t)}$ in $L^{2}(\mathbb{R})$ which
describes a $\delta'$-interaction with time-dependent strength $1/\gamma(t)$.
We prove that the strong solution of such a Cauchy problem exits whenever the
map $t\mapsto\gamma(t)$ belongs to the fractional Sobolev space
$H^{3/4}(\mathbb{R})$, thus weakening the hypotheses which would be required by
the known general abstract results. The solution is expressed in terms of the
free evolution and the solution of a Volterra integral equation.
