A class of inverse problems for fractional order degenerate evolution equations-Reference-Cited by-同舟云学术

A class of inverse problems for fractional order degenerate evolution equations

Published:2020-10-13 Issue:2 Volume:29 Page:173-184
ISSN:1569-3945
Container-title:Journal of Inverse and Ill-posed Problems
language:en
Short-container-title:

Author:

Fedorov Vladimir E.¹^ORCID,Nagumanova Anna V.²,Kostić Marko³

Affiliation:

1. Chelyabinsk State University , Kashirin Brothers St. 129 , Chelyabinsk ; and South Ural State University, Lenin Av. 76, Chelyabinsk , Russia

2. Mathematical Analysis Department , Chelyabinsk State University , Kashirin Brothers St. 129 , Chelyabinsk , Russia

3. Faculty of Technical Sciences , University of Novi Sad , D. Obradović St. 6 , Novi Sad , Serbia

Abstract

Abstract The criteria of the well-posedness is obtained for an inverse problem to a class of fractional order in the sense of Caputo degenerate evolution equations with a relatively bounded pair of operators and with the generalized Showalter–Sidorov initial conditions. It is formulated in terms of the relative spectrum of the pair and of the characteristic function of the problem. Sufficient conditions of the unique solvability are obtained for a similar problem with the Cauchy initial condition. For these purposes the unique solvability of the same inverse problem was studied for the equation with a bounded operator near an unknown function, which is solved with respect to the fractional derivative. General results are applied to the inverse problem research for the time fractional system of equations describing the dynamics of a viscoelastic fluid in the weakly degenerate and the strongly degenerate cases.

Funder

Russian Foundation for Basic Research

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics

Link

https://www.degruyter.com/document/doi/10.1515/jiip-2017-0099/pdf

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