Публикации автора

By the aid of Appell, Humbert and Bessel functions, the integral representations for a Kamp´e de F´eriet function are found. The validity of integral representations for a Kamp´e de F´eriet function of general form are proved. Conditions, under which these representations are expressed in terms of products of two generalized hypergeometric functions are found. Examples, in which the integral representation of the Kamp´e de F´eriet function containing Appell, Humbert or Bessel functions, are identified.

23 ноября 2023 года исполнилось бы 90 лет Салахитдинову Махмуду Салахитдиновичу — видному учёному-математику, доктору физико-математических наук, профессору, академику АН Республики Узбекистан.

In the article the questions of unique solvability and determination of the redefinition coefficient function in the initial inverse problem for two-dimensional Whitham-type partial differential equation with impulse effects are studied. The modified method of characteristics allows partial differential equations of the first order to be represented as ordinary differential equations that describe the change of an unknown function along the line of characteristics. The unique solvability of the two-dimensional inverse problem is proved by the method of successive approximations and contraction mappings. The definition of the unknown coefficient is reduced to solving the Volterra integral equation of the first kind.

25 октября 2024 года исполняется 90 лет со дня рождения академика АН Республики Узбекистан Тухтамурада Джураевича Джураева, известного ученого, специалиста по дифференциальным уравнениям и математическим задачам механики, государственного деятеля науки и образования Узбекистана

In this paper, we consider a nonlinear impulsive parabolic type partial differential equation with nonlinear impulsive conditions. Dirichlet type boundary value conditions with respect to spatial variable is used, and eigenvalues and eigenfunctions of the spectral problem are founded. The Fourier method of the separation of variables is applied. A countable system of nonlinear functional equations is obtained with respect to the Fourier coefficients of the unknown function. A theorem on a unique solvability of the countable system of nonlinear functional equations is proved by the method of successive approximations. A criteria of uniqueness and existence of a solution for the nonlinear impulsive mixed problem is obtained. A solution of the mixed problem is derived in the form of the Fourier series. The absolute and uniform convergence of the Fourier series is proved.