najoNanosystems: Physics, Chemistry, MathematicsНаносистемы: физика, химия, математика2220-80542305-7971Университет ИТМО10.17586/2220-8054-2021-12-3-271-278najo-442Research ArticleMATHEMATICSМАТЕМАТИКАGreen’s function method for time-fractional diffusion equation on the star graph with equal bondsМетод функции Грина для уравнения дробной по времени диффузии на звездном графе с равными ребрамиSobirovZ. A.SobirovZ. A.

Olimlar str., 49, 100041, Tashkent

Universitet str., 4, 100174, Tashkent

z.sobirov@nuu.uzRakhimovK. U.RakhimovK. U.

Universitet str., 4, 100174, Tashkent

kamoliddin_ru@inbox.ruErgashovR. E.ErgashovR. E.

Universitet str., 4, 100174, Tashkent

University of Geological Sciences; National University of UzbekistanUzbekistanNational University of UzbekistanUzbekistan202104082025123271278Copyright © Sobirov Z.A., Rakhimov K.U., Ergashov R.E., 20252025Sobirov Z.A., Rakhimov K.U., Ergashov R.E.Sobirov Z.A., Rakhimov K.U., Ergashov R.E.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/442

This work devoted to construction of the Matrix-Green’s functions of initial-boundary value problems for the time-fractional diffusion equation on the metric star graph with equal bonds. In the case of Dirichlet and mixed boundary conditions we constructed Green’s functions explicitly. The uniqueness of the solutions of the considered problems were proved by the method of energy integrals. Some possible applications in branched nanostructures were discussed.

Данная работа посвящена построению матрицы-функции Грина начально-краевых задач для уравнения дробной по времени диффузии на метрическом звездном графе с равными связями. В случае Дирихле и смешанных краевых условий функции Грина построены явно. Единственность решений рассмотренных задач доказана методом интегралов энергии. Обсуждены некоторые возможные приложения в разветвленных наноструктурах.

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