Geodesic
The time-fractional Airy equation on the metric graph
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 14 (2021) no. 3, pp. 376-388

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Initial boundary value problem for the time-fractional Airy equation on a graph with finite bonds is considered in the paper. Properties of potentials for this equation are studied. Using these properties the solutions of the considered problem were found. The uniqueness theorem is proved using the analogue of Grönwall-Bellman inequality and a-priory estimate.
Keywords: time-fractional Airy equation, IBVP, PDE on metric graphs, fundamental solutions, integral representation. 
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     title = {The time-fractional {Airy} equation on the metric graph},
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     url = {http://geodesic.mathdoc.fr/item/JSFU_2021_14_3_a10/}
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Kamoladdin Rakhimov; Zarifboy Sobirov; Nasridin Zhabborov. The time-fractional Airy equation on the metric graph. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 14 (2021) no. 3, pp. 376-388. http://geodesic.mathdoc.fr/item/JSFU_2021_14_3_a10/