Geodesic
Unique solvability of IBVP for pseudo-subdiffusion equation with Hilfer fractional derivative on a metric graph
Čelâbinskij fiziko-matematičeskij žurnal, Tome 8 (2023) no. 3, pp. 351-370

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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.
Keywords: Hilfer operator, metric graph, method of variables separation, Mittag-Leffler function, a priori estimation, fractional derivatives and integrals. 
@article{CHFMJ_2023_8_3_a3,
     author = {Z. A. Sobirov and J. R. Khujakulov and A. A. Turemuratova},
     title = {Unique solvability of {IBVP} for pseudo-subdiffusion equation with {Hilfer} fractional derivative on a metric graph},
     journal = {\v{C}el\^abinskij fiziko-matemati\v{c}eskij \v{z}urnal},
     pages = {351--370},
     publisher = {mathdoc},
     volume = {8},
     number = {3},
     year = {2023},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CHFMJ_2023_8_3_a3/}
}
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Z. A. Sobirov; J. R. Khujakulov; A. A. Turemuratova. Unique solvability of IBVP for pseudo-subdiffusion equation with Hilfer fractional derivative on a metric graph. Čelâbinskij fiziko-matematičeskij žurnal, Tome 8 (2023) no. 3, pp. 351-370. http://geodesic.mathdoc.fr/item/CHFMJ_2023_8_3_a3/