Mathematical Analysis, Ordinary and Partial Differential Equations, Fractional Calculus, Numerical Analysis, Computational Mathematics, Numerical Functional Analysis, Identification Problems, Theory of Differential and Integral Inequalities and its Applications, Semigroups of Linear Operators and Their Applications to Partial Differential Equations, Theory of Positive Operators and Stability of Difference Schemes, Theory of Interpolation of Operators and its Applications, Difference Schemes for Stochastic Partial Differential Equations, Uniform Difference Schemes for Singular Perturbation Problems, Non-Classical Problems of Mathematical Physics, Well-Posedness of Parabolic and Elliptic Differential and Difference Equations, Stability of the Neutral Delay Differential and Difference Equations, Numerical Solutions of Applied Problems, Secondary School and University Students Mathematical Olympiads.
Main publications:
A. Ashyralyev and P. E. Sobolevskii, Well-Posedness of Parabolic Difference Equations, Operator Theory: Advances and Applications, 69, Birkhäuser Verlag, Basel, Boston, Berlin, 1994
A. Ashyralyev and P. E. Sobolevskii, New Difference Schemes for Partial Differential Equations, Operator Theory: Advances and Applications, 148, Birkhäuser Verlag, Basel, Boston, Berlin, Operator, 2004
A. Ashyralyev and H. O. Fattorini, “On uniform difference schemes for second order singular perturbation problems in Banach spaces”, SIAM J. Math. Analysis, 23:1 (1992), 29–54
A. Ashyralyev, “Nonlocal boundary value problems for abstract parabolic equations: well-posedness in Bochner spaces”, Journal of Evolution Equations, 6:1 (2006), 1–28
A. Ashyralyev, “A note on the Bitsadze-Samarskii type nonlocal boundary value problem in a Banach space”, Journal of Mathematical Analysis and Applications, 344:1 (2008), 557–573
