On the Solvability of a Boundary Value Problem for the Ordinary Fredholm Integrodifferential Equation with a Degenerate Kernel

Yuldashev, T. K.

doi:10.1134/s0965542519020167

Cited by 28 publications

(4 citation statements)

References 13 publications

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“…In [18][19][20][21][22][23][24] the problems of solvability for some type of integro-differential equations with degenerate kernel were considered. Also, a lot of publications of studying on differential equations with impulsive effects, describing many natural and technical processes, are appearing [25][26][27][28][29][30][31][32][33][34][35].…”

Section: Introductionmentioning

confidence: 99%

On a nonlinear impulsive system of integro-differential equations with degenerate kernel and maxima

Yuldashev¹,

Fayziev²

2022

Nanosystems: Phys. Chem. Math.

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A nonlocal boundary value problem for a system of ordinary integro-differential equations with impulsive effects, degenerate kernel and maxima is investigated. The boundary value problem is given by the integral condition. The method of successive approximations in combination with the method of compressing mapping is used. The existence and uniqueness of the solution of the boundary value problem are proved. The continuous dependence of the solution on the right-hand side of the boundary value condition is shown. KEYWORDS impulsive integro-differential equations, nonlocal condition, successive approximations, existence and uniqueness, continuous dependence of solution FOR CITATION Yuldashev T.K., Fayziev A.K. On a nonlinear impulsive system of integro-differential equations with degenerate kernel and maxima.

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Section: Introductionmentioning

confidence: 99%

On a nonlinear impulsive system of integro-differential equations with degenerate kernel and maxima

Yuldashev¹,

Fayziev²

2022

Nanosystems: Phys. Chem. Math.

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“…The issues of solvability of initial and boundary value problems for integro-differential equations are discussed in the works of many authors [3][4][5][6][7][8][9][10].…”

Section: Introductionmentioning

confidence: 99%

On Unique Solvability of a Multipoint Boundary Value Problem for Systems of Integro-Differential Equations with Involution

2022

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In this paper, a multipoint boundary value problem for systems of integro-differential equations with involution has been studied. To solve the studied problem, the parameterization method is used. Based on the parametrization method, the studied problem is decomposed into two parts, i.e., into the Cauchy problem and a system of linear equations. Necessary and sufficient conditions for the unique solvability of the studied problem are determined.

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“…One of the important sections of the theory of integral and differential equations is the theory of integro-differential equations. The presence of an integral term in differential equations of the first and second orders has an important role in the theory of dynamical systems with automatic control [25,26]. Mixed type integer order integro-differential equations with degenerate kernels and spectral parameters are studied in [27,28].…”

Section: Introductionmentioning

confidence: 99%

Mixed type integro-differential equation with fractional order Caputo operators and spectral parameters

Yuldashev

Karimov

2021

Izvestiya Instituta Matematiki I Informatiki Udmurtskogo Gosudarstvennogo Universiteta

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The issues of unique solvability of a boundary value problem for a mixed type integro-differential equation with two Caputo time-fractional operators and spectral parameters are considered. A mixed type integro-differential equation is a partial integro-differential equation of fractional order in both positive and negative parts of multidimensional rectangular domain under consideration. The fractional Caputo operator's order is less in the positive part of the domain, than the order of Caputo operator in the negative part of the domain. Using the method of Fourier series, two systems of countable systems of ordinary fractional integro-differential equations with degenerate kernels are obtained. Further, a method of degenerate kernels is used. To determine arbitrary integration constants, a system of algebraic equations is obtained. From this system, regular and irregular values of spectral parameters are calculated. The solution of the problem under consideration is obtained in the form of Fourier series. The unique solvability of the problem for regular values of spectral parameters is proved. To prove the convergence of Fourier series, the properties of the Mittag-Leffler function, Cauchy-Schwarz inequality and Bessel inequality are used. The continuous dependence of the problem solution on a small parameter for regular values of spectral parameters is also studied. The results are formulated as a theorem.

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On the Solvability of a Boundary Value Problem for the Ordinary Fredholm Integrodifferential Equation with a Degenerate Kernel

Cited by 28 publications

References 13 publications

On a nonlinear impulsive system of integro-differential equations with degenerate kernel and maxima

On a nonlinear impulsive system of integro-differential equations with degenerate kernel and maxima

On Unique Solvability of a Multipoint Boundary Value Problem for Systems of Integro-Differential Equations with Involution

Mixed type integro-differential equation with fractional order Caputo operators and spectral parameters

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