A Problem With Parameter for the Integro-Differential Equations

Бакирова, Е. А.; Assanova, A. T.; Kadirbayeva, Zh. M.

doi:10.3846/mma.2021.11977

Cited by 22 publications

(4 citation statements)

References 21 publications

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“…Ары қарай параметрлеу әдісі дифференциалдық теңдеулердің әртүрлі кластары үшін шеттік есептерді шешуде Д.С. Жұмабаевтың [11,12] және оның оқушыларының жұмыстарында [13][14][15][16][17][18][19][20][21][22] орын алды.…”

Section: кіріспеunclassified

On the Unique Solvability of a Boundary Value Problem for Differential Equations With Parameter

Bakirova,

Iskakova,

Тemesheva

et al. 2024

jour

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A linear boundary value problem for a differential equation with a parameter is investigated on a finite interval by the parameterization method. The studied boundary value problem with parameter is reduced to an equivalent multipoint boundary value problem with parameters by splitting the interval, introducing additional parameters at the points of splitting and new functions. The obtained equivalent boundary value problem contains Cauchy problems for ordinary differential equations with respect to new functions. By substituting the solution representation of the Cauchy problem into the boundary conditions and continuity conditions of the solution, a system of linear algebraic equations with respect to the introduced parameters is compiled. An algorithm for finding a solution to the boundary value problem with parameters is constructed. The formulation of the theorem on sufficient conditions of unique solvability of the boundary value problem with parameters is given. Sufficient conditions of its unique solvability are obtained in terms of the data of the original boundary value problem. An example showing the fulfillment of the conditions of the theorem is given.

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Section: кіріспеunclassified

On the Unique Solvability of a Boundary Value Problem for Differential Equations With Parameter

Bakirova,

Iskakova,

Тemesheva

et al. 2024

jour

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show abstract

“…Loaded differential equations of the form (2.10) with various other types of initial-boundary conditions, as well as the corresponding inverse problems, optimal control problems in various settings have been studied by many authors [4,5,10]. For them, the necessary conditions for the existence and uniqueness of the solution were obtained [7], [16]- [18] and various numerical solution schemes were proposed [3,6,8]. Considering a significant increase in the order of the original problem (2.1) and (2.2), the use of such approaches to the study and solution of practical problems of the form (2.1) and (2.2) and related inverse problems, optimal control problems, causes serious difficulties [4,5,10].…”

Section: Formulation Of the Problemmentioning

confidence: 99%

To the solution of integro-differential equations with nonlocal conditions

2021

Turk J Math

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We investigate linear integro-differential equations with ordinary derivatives. The kernels of the integrands depend only on the variable of integration, and the conditions involve the terms with the point and integral values of the unknown function. We drive necessary and sufficient conditions for the existence and uniqueness of the solution of the problem, which can be used both for analytical and numerical solutions. We present the results of solving an illustrative test problem.

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“…Figure 3Comparison of the effects of different encryption methods on data transmission stability It can be seen from Figure3that the stability of encrypted distributed data transmission increases with the increase in the number of times. The filtering algorithm encryption method is more stable than the clustering algorithm method for distributed data transmission after distributed data encryption[10]. The encryption method in this paper encrypts the distributed data, and the stability of the distributed data transmission is higher than that of the filtering algorithm encryption method.…”

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confidence: 94%

Continuing Education Network Data Center Model Based on Fractional Differential Mathematical Equations

2022

Applied Mathematics and Nonlinear Sciences

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Continuing education platforms are faced with problems such as the aging of online learning platforms and backward technology. The data center network is an essential infrastructure supporting the big data and cloud computing platform continuing education network. It is widely used for data-intensive and massively parallel computing tasks. The paper proposes a continuing education network data center management model based on this research background. At the same time, this paper proposes a real-time encryption method for distributed data in a multi-layer differential continuing education network based on fractional differential mathematical equations. The experimental study found that the fractional differential mathematical equations method can effectively control the stability of data transmission of continuing education receipt networks. This algorithm improves the efficiency of network data operation and controls the cost of encryption. The research results of this paper provide technical support for network education.

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A Problem With Parameter for the Integro-Differential Equations

Cited by 22 publications

References 21 publications

On the Unique Solvability of a Boundary Value Problem for Differential Equations With Parameter

On the Unique Solvability of a Boundary Value Problem for Differential Equations With Parameter

To the solution of integro-differential equations with nonlocal conditions

Continuing Education Network Data Center Model Based on Fractional Differential Mathematical Equations

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