- Qualitative theory of ordinary differential equations.
- Boundary layer theory.
- Mathematical analysis.
- Analytical geometry.
- Linear algebra.
- Equations of mathematical physics.
- Integral equations.
- Theory of potential.
- Boundary value problem for partial differential equation.
- Boundary value problem with non-local and global boundary conditions.
- The theory of difference schemas.
- Numerical methods for solution of problems of mathematical physics.
- Spectral theory.
- Asymptotic methods.
- Discrete analysis.
- Analysis on manifold.
- Ordinary differential equations of fractional order and problems of these equations.
- Fractional order spaces.
- Unordinary analysis.
- Multiplicative analysis.
- Inverse problems in terms of Tikhonov.
- Inverse problems in terms of Stefan.
- Discrete additive-multiplicative and multiplicative-additive theory and its problems.
- Residue method and method of contour integral.
- New mathematics. Operations based on three sequential direct (inverse) actions