STABILITY OF THE TIME-DEPENDENT IDENTIFICATION PROBLEM FOR A FRACTIONAL TELEGRAPH EQUATION WITH THE CAPUTO DERIVATIVE

STABILITY OF THE TIME-DEPENDENT IDENTIFICATION PROBLEM FOR A FRACTIONAL TELEGRAPH EQUATION WITH THE CAPUTO DERIVATIVE

Авторы

  • Radjabovich Institute of Mathematics named after V.I. RomanovskyInstitute of Mathematics named after V.I. Romanovsky
  • Alisherovich Institute of Mathematics named after V.I. Romanovsky

DOI:

https://doi.org/10.52754/16948645_2023_2_166

Ключевые слова:

Телеграфное уравнение, гильбертово пространство, самосопряженный, положительный оператор, производная Капуто

Аннотация

The telegraph equation   , in a Hilbert space  is investigated. Here  is a self-adjoint, positive operator,  is the Caputo derivative. An inverse problem is considered in which, along with , also a time varying factor  of the source function is unknown. To solve this inverse problem, we take the additional condition with an arbitrary bounded linear functional .Existence and uniqueness theorem for the solution to the problem under consideration is proved. Inequalities of stability are obtained.

Библиографические ссылки

Pskhu A.V. Fractional Differential Equations. Moscow: NAUKA. 2005 [in Russian].

Ashyralyev.A., Al-Hazaimeh.M. Stability of the time-dependent identication problem for the Telegraph equation with involution, International Journal of Applied Mathematics, 35, 3, 447--459 ,(2022). DOI: https://doi.org/10.12732/ijam.v35i3.7

Cascaval. R., Eckstein.E., Frota.C., Goldstein.A.,, Fractional telegraph equations, J. Math. Anal. Appl. 276, 145-159 (2002). DOI: https://doi.org/10.1016/S0022-247X(02)00394-3

Загрузки

Опубликован

30-12-2023

Как цитировать

Ashurov , R., & Saparbayev, R. (2023). STABILITY OF THE TIME-DEPENDENT IDENTIFICATION PROBLEM FOR A FRACTIONAL TELEGRAPH EQUATION WITH THE CAPUTO DERIVATIVE: STABILITY OF THE TIME-DEPENDENT IDENTIFICATION PROBLEM FOR A FRACTIONAL TELEGRAPH EQUATION WITH THE CAPUTO DERIVATIVE. Вестник Ошского государственного университета. Математика. Физика. Техника, (2(3), 166–169. https://doi.org/10.52754/16948645_2023_2_166

Выпуск

№ 2(3) (2023): Вестник Ошского государственного университета. Математика. Физика. Техника

Раздел

МАТЕМАТИКА

Лицензия

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