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Izv. RAN. Ser. Mat., 2017, Volume 81, Issue 6, Pages 158–179 (Mi izv8520)  

This article is cited in 1 scientific paper (total in 1 paper)

The first boundary-value problem for a fractional diffusion-wave equation in a non-cylindrical domain

A. V. Pskhu

Federal State Scientific Institution «Institution of Applied Mathematics and Automation», Nal'chik

Abstract: We solve the first boundary-value problem in a non-cylindrical domain for a diffusion-wave equation with the Dzhrbashyan–Nersesyan operator of fractional differentiation with respect to the time variable. We prove an existence and uniqueness theorem for this problem, and construct a representation of the solution. We show that a sufficient condition for unique solubility is the condition of Hölder smoothness for the lateral boundary of the domain. The corresponding results for equations with Riemann–Liouville and Caputo derivatives are particular cases of results obtained here.

Keywords: diffusion-wave equation, first boundary-value problem, fractional derivative, Dzhrbashyan–Nersesyan operator, non-cylindrical domain.

Funding Agency Grant Number
Russian Foundation for Basic Research 16-01-00462
This work was supported by the Russian Foundation for Basic Research (grant no. 16-01-00462).


DOI: https://doi.org/10.4213/im8520

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English version:
Izvestiya: Mathematics, 2017, 81:6, 1212–1233

Bibliographic databases:

UDC: 517.95
MSC: 35R11
Received: 08.02.2016

Citation: A. V. Pskhu, “The first boundary-value problem for a fractional diffusion-wave equation in a non-cylindrical domain”, Izv. RAN. Ser. Mat., 81:6 (2017), 158–179; Izv. Math., 81:6 (2017), 1212–1233

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. F. G. Khushtova, “K probleme edinstvennosti resheniya zadachi Koshi dlya uravneniya drobnoi diffuzii s operatorom Besselya”, Vestn. Sam. gos. tekhn. un-ta. Ser. Fiz.-mat. nauki, 22:4 (2018), 774–784  mathnet  crossref  elib
  • Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya Izvestiya: Mathematics
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