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Department : Matematik Bölümü ✕
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Approximate Solution of the System of Linear Volterra-Stieltjes Integral Equations of the Second Kind

Avıt ASANOV | Kalıskan MATANOVA

A numerical solution of the system of linear Volterra–Stieltjes integral equations of the second kind has been found and analyzed using the so-called generalized trapezoid rule. Conditions for estimating the error have also been determined and justified. A solution of an example obtained using the proposed method is given.

Article 2022 Fen Fakültesi Journal of Mathematical Sciences262 ( 2 ) 56 Views
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SOLUTION OF SOME LINEAR SYSTEMS OF ORDINARY DIFFERENTIAL EQUATIONS WITH VARIABLE COEFFICIENTS

Anarkül URDALETOVA

The problem of integrability of ordinary differential equations to find their exact solutions is a celebrated problem in the theory of differential equations which attracted attention of several workers in the area. This is due to the fact that: (a) differential equations are the most widely used continuous models of dynamic systems in physics, medicine, economics, biology and other sciences that study the surrounding reality, for which the explicit trajectory of the dynamic system's behavior is important as the explicit solution contains in itself the maximum information about the behavior of ...More

Article 2022 Fen Fakültesi Advances in Differential Equations and Control Processes29 17 Views
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Fekete-Szegö inequality for a subclass of analytic functions associated with Gegenbauer polynomials

Muhammet KAMALİ

In this paper, we define a subclass of analytic functions by denote (Formula Presented) satisfying the following subordinate condition (Formula Presented) where (Formula Presented). We give coefficient estimates and Fekete-Szegö inequality for functions belonging to this subclass.

Article 2022 Fen Fakültesi Carpathian Mathematical Publications14 ( 2 ) 10 Views
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Introduction to Linear Difference Equations

Anarkül URDALETOVA

One of the biggest problems of modern mathematics is, to a large extent, its isolation from the world around it. Extensive use of linear difference equations can make a great contribution to solving this problem. In the language of these equations, the problems of financial mathematics are beautifully presented. And as can be understood from the study of difference equations, this is by no means their only advantage. In particular, there is a direct connection between the theory of linear difference equations and the theory of linear ordinary differential equations. Therefore, we are convinced ...More

Chapter of Books 2022 Fen Fakültesi Advances in Mathematics Research32 ( Chapter 5 ) 22 Views
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Method of additional argument in problems of optimal control

Ramiz RAFATOV

The problem of control of the process described by the nonlinear differential equation with partial derivatives of the first order, with conditions at t 0 and in a sequence n of points x1 < x2 ... < xn is solved. The criterion of quality of control is the integrated quadratic functional, which depends on a final state of system and set n of controlling parameters. The method of increment of functional is applied to reception of conditions of optimality, and the method of additional argument (MAA) is applied for the decision of the nonlinear equations with partial derivatives.

Proceedings Paper 2004 Fen Fakültesi IFAC Proceedings Volumes (IFAC-PapersOnline)37 ( 17 ) 9 Views
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The Optimal Vector Control for the Elastic Oscillations Described by Fredholm Integral-Differential Equations

Elmira ABDILDAYEVA

In this paper, we investigate the nonlinear problem of the optimal vector control for oscillation processes described by Fredholm integro-differential equations in partial derivatives when function of external sources nonlinearly depend on control parameters. It was found that the system of nonlinear integral equations,which obtained relatively to the components of the optimal vector control, have the property of equal relations. This fact lets us to simplify the procedure of the constructing the solution of the nonlinear optimization problem. We have developed algorithm for constructing the s ...More

Proceedings Paper 2019 Fen Fakültesi Analysis and Partial Differential Equations: Perspectives from Developing Countries275 17 Views
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University Learners’ Motivation and Experiences Using Virtual Laboratories in a Physics Course

Azat AKMATBEKOVA | Gülşat MUHAMETJANOVA

It is becoming necessary to examine learners’ use of and experiences with virtual laboratories. Learners’ interest and motivation to use virtual laboratories are important factors for the success of these platforms. This study was conducted to analyze Kyrgyz learners’ use of virtual laboratories in a physics course at the university level. The study was performed in the 2019–2020 spring term at a state university in Kyrgyzstan. The study took a quantitative approach, with 376 Kyrgyz learner participants studying at the undergraduate level. The participants were divided into three groups: the f ...More

Article 2022 Fen Fakültesi Canadian Journal of Learning and Technology (CJLT)48 ( 2 ) 49 Views
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Using the Cramer-Gauss Method to Solve Systems of Linear Algebraic Equations with Tridiagonal and Five-Diagonal Coefficient Matrices

Anarkül URDALETOVA

It is known that among the methods used in solving systems of linear algebraic equations, the Cramer method has a number of disadvantages compared to the Gauss method, in particular: the inability to write out solutions to a system that has many solutions; the cumbersomeness of calculations with large system size. However, when applied to systems with a square matrix, it is, in a sense, more convenient than the Gauss method. The authors of this work developed and proposed a method in which they tried to combine the advantages of the Cramer and Gauss methods. In this paper, the Cramer-Gauss met ...More

Proceedings Paper 2023 Fen Fakültesi Intelligent Systems and Applications3 61 Views
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On the Solvability of the Synthesis Problem for Optimal Control Systems with Distributed Parameters

Elmira ABDILDAYEVA

The solvability of synthesis problem of external and boundary controls is investigated for optimization of oscillation process, described by partial differential equations with Fredholm integral operator. Functions of the external and boundary actions are nonlinearly with respect to control. An integro-differential equation is obtained in the specific type for Bellman functional. An algorithm is developed for constructing solutions to synthesis problem of external and boundary controls. Keywords: Generalized solution, Bellman functional, Frechet differential, Integro-differential equation, Fre ...More

Chapter of Books 2022 Fen Fakültesi Trends in Mathematics 59 Views
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On the solvability of a nonlinear optimization problem with boundary vector control of oscillatory processes = О разрешимости задачи нелинейной оптимизации при граничном векторном управлении колебательными процессами = Тербелмелi процестердi шекаралық векторлық басқарумен сызықтыемес оңтайландыру есебiнiң шешiмi туралы

Elmira ABDILDAYEVA

In the paper, the solvability of the nonlinear boundary optimization problem has been investigated for the oscillation processes, described by the integro-differential equation in partial derivatives with Fredholm integral operator. It has been established that the components of the boundary vector control are defined as a solution to a system of nonlinear integral equations of a specific form, and the equations of this system have the property of equal relations. An algorithm for constructing a solution to the problem of nonlinear optimization has been developed. Keywords: general solution; n ...More

Article 2023 Fen Fakültesi Bulletin of the Karaganda University - Mathematics / Вестник Карагандинского университета. Серия Математика109 ( 1 ) 38 Views
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О методе функционалов Ляпунова для линейного вольтеррова интегродифференциального уравнения первого порядка с запаздыванием на полуоси

Samandar İSKANDAROV

Устанавливаются достаточные условия, обеспечивающие оценку, ограниченность, степенную абсолютную интегрируемость на полуоси, стремление к нулю при стремлении к бесконечности независимой переменной всех решений линейного вольтеррова интегродифференциального уравнения первого порядка с запаздыванием. Для этого строится обобщенный функционал Ляпунова. Приводится иллюстративный пример. Keywords: volterra integrodifferential equation of the first order; argument lag; estimation; boundedness; absolute integrability; tending to zero of solutions; generalized method of lyapunov functionals

Article 2023 Fen Fakültesi Вестник Московского университета. Серия 1: Математика. Механика ( 3 ) 17 Views
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Выбор параметров решения линейных неклассических уравнений первого рода

Avıt ASANOV

В рассматриваемой работе выбран параметр регуляризации для решения линейного интегрального уравнения Вольтерра первого рода. Во многих работах были исследованы различные вопросы для интегральных уравнений. Даже когда уравнение первого типа Вольтерры является интегральным уравнением с точным выходом, неклассические уравнения, интегрируемые по предел, являются линейными, и нелинейные интегральные уравнения являются линейными, и это обусловлено необходимостью разработки новых методов для единственности их решений. Но в данной работе получены основополагающие результаты для интегральных уравнений ...More

Article 2023 Fen Fakültesi Бюллетень науки и практики / Bulletin of Science and Practice9 ( 4 ) 27 Views
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