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

Abstract

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.

Existence and uniqueness theorem for a weak solution of fractional parabolic problem by the Rothe method

“…They prove the existence and uniqueness of the solution by using the Lax-Milgram Lemma in some suitable Sobolev spaces. Paper [17] dealt with a time fractional equation on the metric star graph. The authors applied the method of energy integrals to construct Green's matrix-function and discussed applications to nanostructures.…”

Spectral gaps for star-like quantum graph and for two coupled rings

“…But using of such approaches is not simple due to great computational complexity. The situation changes if a particle under consideration cannot leave a submanifold of less dimension [1][2][3][4]. It allows one to reduce the problem to a task on this manifold or several manifolds [5].…”