A Cauchy Type Problem for a Degenerate Equation with the Riemann–Liouville Derivative in the Sectorial Case
- 作者: Fedorov V.E.1, Avilovich A.S.2
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隶属关系:
- Chelyabinsk State University, South Ural State University
- Chelyabinsk State University
- 期: 卷 60, 编号 2 (2019)
- 页面: 359-372
- 栏目: Article
- URL: https://journals.rcsi.science/0037-4466/article/view/172371
- DOI: https://doi.org/10.1134/S0037446619020162
- ID: 172371
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详细
Under study is the unique solvability of a Cauchy type problem and a generalized Schowalter–Sidorov type problem for a class of linear inhomogeneous equations in Banach spaces with a degenerate operator at the Riemann–Liouville fractional derivative. We find an explicit form of a solution under some conditions for the pair of operators in the equation. To this end, we study a Cauchy type problem for an equation solvable with respect to the Riemann–Liouville derivative with an operator on the right-hand side which generates a resolving family of operators analytic in a sector. These abstract results are used to prove the unique solvability of an initial-boundary value problem for the Navier–Stokes system of equations of fractional order in time.
作者简介
V. Fedorov
Chelyabinsk State University, South Ural State University
编辑信件的主要联系方式.
Email: kar@csu.ru
俄罗斯联邦, Chelyabinsk
A. Avilovich
Chelyabinsk State University
编辑信件的主要联系方式.
Email: avilovich_aas@bk.ru
俄罗斯联邦, Chelyabinsk
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