  The spectrum profile that emerges in molecular spectroscopy and atmospheric
radiative transfer as the combined effect of Doppler and pressure broadenings
is known as the Voigt profile function. Because of its convolution integral
representation, the Voigt profile can be interpreted as the probability density
function of the sum of two independent random variables with Gaussian density
(due to the Doppler effect) and Lorentzian density (due to the pressure
effect). Since these densities belong to the class of symmetric L\'evy stable
distributions, a probabilistic generalization is proposed as the convolution of
two arbitrary symmetric L\'evy densities. We study the case when the widths of
the considered distributions depend on a scale-factor $\tau$ that is
representative of spatial inhomogeneity or temporal non-stationarity. The
evolution equations for this probabilistic generalization of the Voigt function
are here introduced and interpreted as generalized diffusion equations
containing two Riesz space-fractional derivatives, thus classified as
space-fractional diffusion equations of double order.
