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Index Type : ESCI ✕Department : Matematik Bölümü ✕
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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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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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On the Method of Lyapunov Functionals for a Linear First-Order Volterra Integrodifferential Equation with Delay on the Semiaxis

Samandar İSKANDAROV

Sufficient conditions are established to ensure the estimation, boundedness, power-law absolute integrability on the semiaxis, the tendency to zero under the tendency to infinity of the independent variable of all solutions of the linear Volterra integrodifferential equation of the first order with delay. For this purpose, a generalized Lyapunov functional is constructed. An illustrative example is presented. Keyword: absolute integrability; argument lag; boundedness; estimation; generalized method of Lyapunov functionals; tending to zero of solutions; Volterra integrodifferential equation of ...More

Article 2023 Fen Fakültesi Moscow University Mathematics Bulletin78 ( 3 ) 18 Views
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On the upper bounds of Hankel determinants for some subclasses of univalent functions associated with sine functions

Muhammet KAMALİ | Alina RISKULOVA

Let a normalized analytic function be given on the open unit disk. In this paper, we define and consider some familiar subsets of analytic functions associated with sine functions in the region of unit disk on the complex plane. For these classes, we aim to find the upper bounds of the modules of the Hankel determinants obtained from the coefficients of the functions belonging to some classes defined by subordination. Keyword: analytic functions; coefficient estimates; convex function; hankel determinant; sine function; starlike functions; subordination

Article 2024 Fen Fakültesi International Journal of Optimization and Control: Theories & Applications14 ( 1 ) 4 Views
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Fekete-Szego Problem for a Subclass of Analytic Functions Associated with Chebyshev Polynomials

Muhammet KAMALİ

In this paper, we obtain initial coefficients vertical bar a(2)vertical bar and vertical bar a(3)vertical bar for a certain subclass by means of Chebyshev polynomials expansions of analytic functions in D. Also, we solve Fekete-Szego problem for functions in this subclass.

Article 2022 Fen Fakültesi Boletim da Sociedade Paranaense de Matemática40 68 Views
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ON BOUNDS OF TOEPLITZ DETERMINANTS FOR A SUBCLASS OF ANALYTIC FUNCTIONS

Muhammet KAMALİ | Alina RISKULOVA

In the present article, our aim is to investigate the problem of obtaining upper bounds for T2(2), T2(3), T3(2) and T3(1), which are special cases of the symmetric Toeplitz determinant for functions belonging to the M(A, n) subclass. Keyword: convex function; hankel determinant; starlike function; toeplitz determinant; univalent function

Article 2022 Fen Fakültesi Bulletin of Mathematical Analysis and Applications14 ( 3 ) 29 Views
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On Subordination Results for Certain Classes of Analytic Functions of Reciprocal Order

Muhammet KAMALİ | Alina RISKULOVA

In this paper, we introduce the subclass S-beta (alpha, lambda) of analytic functions and obtain coefficient inequality for functions belong to this class. Furthermore, we give sufficient conditions for starlikeness of reciprocal order of analytic functions. In the last part, we obtain the subordination results of a new subclass of analytic functions of reciprocal order, which are defined here by means of a Hadamard product of analytic functions. The results presented in this work improve or generalize the recent works of other authors and also give rise to several new results.

Article 2021 Fen Fakültesi International Journal of Analysis and Applications19 ( 1 ) 46 Views
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About Power Absolute Integrated of the Solution of Volterra System of Linear Second Kind Integral Equations on Half-axis

Samandar İSKANDAROV

Sufficient conditions are established such as the sign of the functions of absolute and quadratic integrability on the half-axis of the components of the solution of a linear system of Volterra-type integral equations of the second kind in the new formulation, namely, without the assumption that the components of the free term possess the properties under study. To achieve the intended goals, the matrix method of weight functions, the matrix method of cutting functions, the matrix method of partial cutting of the author, and the method of integral inequalities of Ya. V. Bykov are developed. Th ...More

Article 2021 Fen Fakültesi Lobachevskii Journal of Mathematics42 ( 3 ) 98 Views
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One Class of Linear Fredholm Operator Equations of the Third Kind

Avıt ASANOV | Kalıskan MATANOVA

In this paper, we are applied a new approach to prove that the solution of the linear Fredholm operator equation of the third kind given on a segment and having a finite number of multipoint singularities is equivalent to the solution of the linear Fredholm operator equation of the second kind with additional conditions. We are showed an example of solving the system of linear integral Fredholm equations of the third kind based on the equivalence of the above equations.

Article 2021 Fen Fakültesi Lobachevskii Journal of Mathematics42 ( 3 ) 66 Views
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Specific Asymptotic Stability of Solutions to a Linear Homogeneous Volterra Integro-Differential Equation of the Fourth Order

Samandar İSKANDAROV

Sufficient conditions for the asymptotic stability of solutions to a fourth-order linear homogeneous Volterra integro-differential equation are established in the case where any nonzero solution to the corresponding linear homogeneous differential equation of the fourth order is not asymptotically stable. An illustrative example is given.

Article 2021 Fen Fakültesi Moscow University Mathematics Bulletin76 ( 1 ) 96 Views
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Solving a System of Linear Algebraic Equations with a Tridiagonal Matrix: A New Look at Cramer's Rule

Anarkül URDALETOVA

To numerically solve a system of linear algebraic equations with a tridiagonal matrix, a recursive version of Cramer's rule is proposed. This method requires no additional restrictions on the matrix of the system similar to those formulated for the double-sweep method. The results of numerical experiments on a large set of test problems are presented. A comparative analysis of the efficiency of the method and corresponding algorithms is given.

Article 2021 Fen Fakültesi Numerical Analysis and Applications14 ( 3 ) 60 Views
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