Nonlocal problem for a nonlinear fractional mixed type integro-differential equation with spectral parameters

Yuldashev, T. K.; Rakhmonov, Farhod D.

doi:10.1063/5.0057147

Cited by 2 publications

(2 citation statements)

References 36 publications

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“…Although the functions (26) are the Fourier coefficients of the solution to the direct problem ( 1)-( 3), they contain extra quantities τ i n r that are still unknown. To find these quantities, we substitute ( 26) into ( 18) and arrive at a new SAE:…”

Section: Formal Solution Of the Direct Problem (1)-(3)mentioning

confidence: 99%

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Inverse Problem for a Hyperbolic Integro-Differential Equation with two Redeﬁnition Conditions at the End of the Interval and Involution

Yuldashev,

Kilichev

2024

Az. J. Math.

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In this paper, we consider an inhomogeneous hyperbolic type partial integrodifferential equation with degenerate kernel, two redefinition functions and involution. Intermediate data are used to find these redefinition functions. Dirichlet boundary conditions with respect to spatial variable are used. The Fourier method of separation of variables is applied. The countable system of functional-integral equations is obtained. Theorem on a unique solvability of countable system of functional-integral equations is proved. The method of successive approximations is used in combination with the method of contraction mappings. The triple of solutions of the inverse problem is obtained in the form of Fourier series. Absolute convergence of Fourier series is proved.

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Section: Formal Solution Of the Direct Problem (1)-(3)mentioning

confidence: 99%

“…Taking into account the known properties of the matrix Θ i r m n (ν, ω), we use the modified Cramer method on the set Λ i2 and obtain the solutions of SAE (27) in the form 29) into (26), we obtain…”

Section: Formal Solution Of the Direct Problem (1)-(3)mentioning

confidence: 99%

Inverse Problem for a Hyperbolic Integro-Differential Equation with two Redeﬁnition Conditions at the End of the Interval and Involution

Yuldashev,

Kilichev

2024

Az. J. Math.

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Нелокальная Краевая Задача Для Одного Дифференциального Уравнения Псевдопараболического Типа Высокого Порядка

Рахмонов

2024

ВОГУМФТ

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Рассмотрены вопросы разрешимости нелокальной краевой задачи для одного псевдопараболического дифференциального уравнения. С помощью метода ряда Фурье получена счетная система обыкновенных интегральных уравнений Фредгольма второго рода для определения коэффициентов неизвестной функции. При доказательстве однозначной разрешимости счетной системы применен метод последовательных приближений в сочетании его с методом сжимающих отображений. Показаны абсолютная и равномерная сходимость и возможность почленного дифференцирования полученных рядов Фурье. Результаты работы сформулированы в виде теорем.

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Nonlocal problem for a nonlinear fractional mixed type integro-differential equation with spectral parameters

Cited by 2 publications

References 36 publications

Inverse Problem for a Hyperbolic Integro-Differential Equation with two Redeﬁnition Conditions at the End of the Interval and Involution

Inverse Problem for a Hyperbolic Integro-Differential Equation with two Redeﬁnition Conditions at the End of the Interval and Involution

Нелокальная Краевая Задача Для Одного Дифференциального Уравнения Псевдопараболического Типа Высокого Порядка

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