  The equation $v=v_0+\int_0^t(t-s)^{\lambda -1}v(s)ds$ is considered,
$\lambda\neq 0,-1,-2...$ and $v_0$ is a smooth function rapidly decaying with
all its derivatives. It is proved that the solution to this equation does
exist, is unique and is smoother than the singular function $t^{-\frac 5 4}$.
