Some remarks on stable densities and operators of fractional differentiation

Details Some remarks on stable densities and operators of fractional differentiation Some remarks on stable densities and operators of fractional differentiation

2004-04-30

arxiv.org/abs/math/0404558v1

Mathematics

Classical Analysis and ODEs

Scientific paper

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

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