Rakhimzhon Zunnunov

Институт математики Академии Наук Республики Узбекистан · Дифференциальные уравнения и их приложения

A boundary value problem of the Bitsadze-Samarskii type is studied in the article for a fractionalorder diffusion equation and a degenerate hyperbolic equation with singular coefficients at lower terms in an unbounded domain. The article considers a mixed domain where the parabolic part of the domain under consideration coincides with the upper hal...

This research explores nonlocal problems associated with fractional diffusion equations and degenerate hyperbolic equations featuring singular coefficients in their lower-order terms. The uniqueness of the solution is established using the energy integral method, while the existence of the solution is equivalently reduced to solving Volterra integr...

In this paper, we study nonlocal problems for a fractional diffusion equation and a degenerate hyperbolic equation with singular coefficients in the lower terms. The uniqueness of the solution to the problem is proved by the method of energy integrals. The existence of a solution is equivalently reduced to the question of the solvability of Volterr...

We consider the problem of Bitsadze–Samarskii type for a generalized Tricomi equation with a spectral parameter in the case where the equation is elliptic in the first quadrant of the plane. We establish the existence and uniqueness of a solution to the problem.

This article studies a problem with shift in the characteristics of different families in an unbounded domain for a mixed-type model equation of the second kind. The elliptic part of this problem is the vertical halfstrip; the hyperbolic part is the characteristic triangle bounded by the characteristics of the equation. Using the extremum principle...

The present paper presents a study on a problem with a fractional integro-differentiation operator in the boundary condition for an equation with a partial Riemann-Liouville fractional derivative. The unique solvability of the problem is proved. In the hyperbolic part of the considered domain, the functional equation is solved by the iteration meth...

The paper investigates the dynamic modes of the Sel’kov fractional self-oscillating system in order to simulate the interaction of cracks. The spectra of the maximum Lyapunov exponents, constructed depending on the parameters of the dynamic system, are used as a research tool. The maximum Lyapunov exponents were constructed according to the Benetti...

В данной статье изучена нелокальная задача для обобщенного уравнения Трикоми со спектральным параметром в неограниченной области эллиптическая часть которой является верхней полуплоскостью. Единственность решения поставленной задачи доказана методом интегралов энергии. Существование решения поставленной задачи доказана методом функций Грина и интег...

In this work, an analogue of the Tricomi problem for equations of mixed type with a fractional derivative is investigated. In one part of the domain, the considered equation is a subdiffusion equation with a fractional derivative of order ? 2 (0; 1) in the sense of Riemann-Liouville, and in the other it is a wave equation. Assuming the parameter ?...

In this paper the inverse problem of determining the fractional orders in mixed-type equations is considered. In one part of the domain the considered equation is the subdiffusion equation with a fractional derivative in the sense of Gerasimov-Caputo of the order 0<a<1 , and in the other part - a wave equation with a fractional derivative of the or...

An initial-boundary value problem for the subdiffusion equation with an elliptic operator A(D) in R N is studied in the article. Existence and uniqueness theorems for the problem under study are proved by the Fourier method. Considering the order of the Riemann-Liouville time-fractional derivative as an unknown parameter, an inverse problem of dete...

Microseismic phenomena are studied by a Sel'kov generalized nonlinear dynamic system. This system is mainly applied in biology to describe substrate and product glycolytic oscillations. Thus, Sel'kov dynamic system can also describe interaction of two types of fractures in an elastic-friable medium. The first type includes seed fractures with lower...

В данной работе для обобщенного уравнения Трикоми со спектральным параметром в неограниченной области эллиптическая часть которой является горизонтальной полосой исследуется задача со смещением на характеристиках разных семейств. Единственность решения задачи доказывается методом интегралов энергии, а существование решения задачи методом функций Гр...

An initial-boundary value problem for a subdiffusion equation with an elliptic operator A(D) in R^n is considered. Uniqueness and existence theorems for a solution of this problem are proved by the Fourier method. Considering the order of the Caputo time-fractional derivative as an unknown parameter, the corresponding inverse problem of determining...

В данной работе для уравнения смешанного типа в неограниченной области эллиптическая часть которой является горизонтальной полосой исследуется задача со смещением на характеристиках разных семейств. Единственность решения задачи доказывается методом интегралов энергии, а существование решения задачи методом функций Грина и методом интегральных урав...

В этой работе в смешанной области, эллиптическая часть которой вертикальная полуполоса, исследована нелокальная задача, в которых нелокальные условия поточечно связывают значения дробной производной искомой функции в точках одной граничной характеристики.

In an article for mixed-type equation in an unbounded domain elliptic part is a rectangle, the unique solvability of a nonlocal boundary value problem. The uniqueness of the solution is proved by energy integrals, and the existence of the method of integral equations

In this paper the existence and uniqueness of the solution of the non-local boundary value problem for the mixed type equation in unbounded domain are proved.In this paper the existence and uniqueness of the solution of the non-local boundary value problem for the mixed type equation in unbounded domain are proved.