Unique solvability of IBVP for pseudo-subdiffusion equation with Hilfer fractional derivative on a metric graph

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 $\delta$-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.