  This work is an attempt to transfer to biology the methods developed in
physics for formulating and solving the kinetic equations in which the kernel
of the integral operator in spatial coordinates is slowly decreasing with
increasing distance and belongs to the class of Levy distributions. An
algorithm is proposed for the reconstruction of the step-length probability
density function (PDF) on a moderate number of trajectories of biological
objects (migrants) and for the derivation of the Green's function of the
corresponding integro-differential kinetic equation for the density of migrants
in the entire space-time range, including the construction of an approximate
self-similar solution. A wide class of time-dependent superdiffusion processes
with a model power-law step-length PDF is considered, which corresponds to
"Levy walks with rests" for given values of the migrant's constant velocity and
the average time T of the migrant's stay between runs. The algorithm is tested
within the framework of a synthetic diagnostics, consisting in the generation
of artificial experimental data for trajectories of migrants and the subsequent
reconstruction of the parameters of the step-length PDF and T. For different
volumes of synthetic data, to obtain a general idea of the distributions under
study (non-parametric case) and to evaluate the accuracy of recovering the
parameters of the PDF (in the case of a parametric representation), the method
of balanced identification is used. The approximate self-similar solution for
the parameters of step-length PDF and T is shown to provide reasonable accuracy
of the space-time evolution of migrant's density.
