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Some remarks on stable densities and operators of fractional differentiation

Yuri A. Neretin
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Abstract

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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Yuri A. Neretin. 2004-04-30. Some remarks on stable densities and operators of fractional differentiation. https://arxiv.org/abs/math/0404558

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