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NANOSYSTEMS: PHYSICS, CHEMISTRY, MATHEMATICS, 2021, 12 (3), P. 271–278

Green’s function method for time-fractional diffusion equation on the star graph with equal bonds

Z. A. Sobirov – University of Geological Sciences, Olimlar str., 49, 100041, Tashkent; National University of Uzbekistan, Universitet str., 4, 100174, Tashkent, Uzbekistan; z.sobirov@nuu.uz
K. U. Rakhimov – National University of Uzbekistan, Universitet str., 4, 100174, Tashkent, Uzbekistan; kamoliddin_ru@inbox.ru
R. E. Ergashov – National University of Uzbekistan, Universitet str., 4, 100174, Tashkent, Uzbekistan

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.

Keywords: Time-fractional diffusion equation, IBVP, PDE on metric graphs, Green’s function.

PACS 02.30.Jr, 02.30.Em

DOI 10.17586/2220-8054-2021-12-3-271-278

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