Some remarks on stable densities and operators of fractional differentiation

Let $D(s)$ be a fractional derivation of order $s$. For a real $p\mathrm{\ne }0$, we construct an integral operator $A(p)$ in an appropriate functional space such that $A(p)D(s)A(p{)}^{-1}=D(ps)$ for all $s$. The kernel of the operator $A(p)$ is expressed in terms of a function similar to the stable densities.