najoNanosystems: Physics, Chemistry, MathematicsНаносистемы: физика, химия, математика2220-80542305-7971Университет ИТМО10.17586/2220-8054-2024-15-5-586-596najo-94Research ArticleMATHEMATICSМАТЕМАТИКАInverse source problem for the subdiffusion equation with edge-dependent order of time-fractional derivative on the metric star graphОбратная задача источника для уравнения субдиффузии с зависящим от ребра порядком дробной производной по времени на метрическом звездообразном графеSobirovZarifboy A

Zarifboy A. Sobirov 

Universitet str., 4, 100174, Tashkent; 100174, Tashkent

https://orcid.org/0009-0003-5428-3958TuremuratovaAriukhan A.

Ariukhan A. Turemuratova

Universitet str., 4, 100174, Tashkent; 100164, Tashkent

ariuxanturemuratova@gmail.comNational University of Uzbekistan; V. I. Romanovskiy Institute of Mathematics, Uzbekistan Academy of ScienceUzbekistanNational University of Uzbekistan; Branch of Russian Economic University named after G. V. Plekhanov in TashkenUzbekistan202403062025155586596Copyright © Sobirov Z.A., Turemuratova A.A., 20252025Sobirov Z.A., Turemuratova A.A.Sobirov Z.A., Turemuratova A.A.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://nanojournal.ifmo.ru/jour/article/view/94

The paper discusses the inverse source problem for the subdiffusion equation in the Sobolev space. The direct and inverse problems are transformed into operator equations to derive solutions. The uniqueness and existence of a strong solution to the direct problem are proven. The inverse problem is reduced to an operator equation, and the well-definedness and continuity of the corresponding resolvent operator are proven.

В статье обсуждается обратная задача источника для уравнения субдиффузии в пространстве Соболева. Для исследования разрешимости прямая и обратная задачи преобразуются в операторные уравнения. Доказаны единственность и существование сильного решения прямой задачи. Обратная задача сводится к операторному уравнению, и доказан непрерывность соответствующего оператора-резольвенты.

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The authors declare that there are no conflicts of interest present.