  Fractional relaxation equations, as well as relaxation functions time-changed
by independent stochastic processes have been widely studied (see, for example,
\cite{MAI}, \cite{STAW} and \cite{GAR}). We start here by proving that the
upper-incomplete Gamma function satisfies the tempered-relaxation equation (of
index $\rho \in (0,1)$); thanks to this explicit form of the solution, we can
then derive its spectral distribution, which extends the stable law.
Accordingly, we define a new class of selfsimilar processes (by means of the
$n$-times Laplace transform of its density) which is indexed by the parameter
$\rho $: in the special case where $\rho =1$, it reduces to the stable
subordinator. Therefore the parameter $\rho $ can be seen as a measure of the
local deviation from the temporal dependence structure displayed in the
standard stable case.
