Objectives. Recently, interest in studying local nonequilibrium processes has increased in the context of the development of laser technologies, the possibility of reaching ultrahigh temperatures and pressures, and the need for a mathematical description of various physical processes under extreme conditions. In simulating local nonequilibrium processes, it becomes necessary to take into account the internal structure of investigation subjects, which significantly complicates the classical

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... port models. An important stage here is to construct mathematical models of various physical fields in which their spatiotemporal nonlocality should be taken into account. For these purposes, hyperbolic equations are used for a wide class of phenomena and, first of all, for unsteady-state heat conduction processes based on the generalized Maxwell–Cattaneo–Luikov–Vernotte phenomenology. Mathematical models in the form of boundary value problems for hyperbolic equations are called generalized boundary value problems. These problems differ significantly in solving difficulty from the classical ones based on Fourier phenomenology. The specificity of these problems is the relative simplicity of the initial mathematical models, together with the difficulty of solving them in an analytically closed form. Hence, very little success has been achieved in finding exact analytical solutions to problems of this kind. The most acceptable approach to solving them is operational calculus. However, it gives analytical solutions in the Laplace transform space as complex functional structures, the inverse transforms of which are not available in well-known reference books on operational calculus. On this path, serious computational difficulties arise. The study aimed to analyze a set of nonstandard transforms arising from the operational solution of mathematical models of local nonequilibrium heat transfer and to obtain their inverse transforms.Methods. Methods and theorems of operational calculus, methods of contour integration of complex t [...]