«Harmonic analysis and theory of functions approximation by polynomials: series and Fourier integrals, positive-definite functions and splines, direct theorems on the approximation of functions by polynomials with different constraints».
«Pompeiu problem and its application to different issues of the functions theory and integral geometry».
«Operator expansions theory, the interpolation problems, the problem of moments».
«Spectral theory of differentiation operators – inverse problem, operators similarity, issues of root vectors system completeness».
«Qualitative properties of solutions of singular, spectral, non-classical problems for elliptic and evolutional equations and variational inequalities».
«Modelling heuristic-didactic systems».
«Methods of integration of differential equations of solids dynamics on invariant manifolds».
«Mathematical modelling and managing natural, physical and economic systems»
«Stochastic differential equations and their applications for dynamics of real processes modelling»
«Application of indistinct calculus theory, management and estimation in finance».
«Mathematical models and methods in the problems of wave dynamics of deformable bodies and structure elements with complicated physical-mechanical properties».
«Mathematical modelling in non-classical problems of theory of straining and strength of multiply-connected anisotropic media with apertures and cracks under the effect of complex conjugate physical-mechanical fields».
«Methods, models and information technologies of visual and auditory images recognition».
«Development of mathematical methods of research of strength and resistance of thin-slab structures under the effect of different force and thermal fields».
«Dynamics and stability of motion of solids with elastic compartments containing fluid».