In the early 1940s, in analyzing the Brownian motion of physical systems of particles, Kolmogorov deduced an ultraparabolic equation for the probability density of possible values of coordinates of the system and their time derivatives [1]. Later, it was discovered that this equation is very important for the investigation of thermal and diffusion processes with inertia in homogeneous media. The appearance of this equation stimulated the development of both the theory of ultraparabolic Kolmogorov-type equations and the general theory of degenerate Kolmogorovtype parabolic equations of any order. Numerous Ukrainian and foreign mathematicians gave significant attention to the development of these theories (see the survey in [2]) mainly by generalizing the well-known classes of ultraparabolic Kolmogorov-type equations, introducing new classes of equations (by increasing the order of equation, generalizing the parabolicity of its nondegenerate part, weakening conditions imposed on the coefficients of the equation, taking into account the possibility of appearance of various types of degenerations with respect to the time variable in the equation, etc.), and the construction of the fundamental solution, analysis of its properties, and investigation of possible applications. In [3], we consider a new class of degenerate equations generalizing the Kolmogorov diffusion equation with inertia. These equations have the form