UNIQUE SOLVABILITY OF IBVP FOR PSEUDO-SUBDIFFUSION EQUATION WITH HILFER FRACTIONAL DERIVATIVE ON A METRIC GRAPH
Z. A. SobirovNational University of Uzbekistan; V.I. Romanovskiy Institute of MathematicsJ.R. KhujakulovV.I. Romanovskiy Institute of Mathematics; Chirchik State Pedagogical UniversityA. A. TuremuratovaNational University of Uzbekistan; Tashkent Branch of Russian University of Economics named after G.V. Plekhanov
ABI
Аннотация
In this paper, we investigate an initial boundary-value problem for a pseudo-subdiffusion equation involving the Hilfer time-fractional derivative on a metric graph. At the boundary vertices of the graph, we used the Dirichlet condition. At the branching points (inner vertices) of the graph, we use δ-type conditions. Such kind of conditions ensure a local flux conservation at the branching points and are also called Kirchhoff conditions. The uniqueness of a solution of the considered problem is shown using the so-called method of energy integrals. The existence of a regular solution to the considered problem is proved. The solution is constructed in the form of the Fourier series.
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