Open AccessLinear Inverse Problems for Multi-term Equations with Riemann — Liouville Derivatives
Author(s) -
М. М. Turov,
AUTHOR_ID,
В. Е. Федоров,
Bùi Trọng Kiên,
AUTHOR_ID,
AUTHOR_ID
Publication year - 2021
Publication title -
izvestiâ irkutskogo gosudarstvennogo universiteta. seriâ "matematika"/izvestiâ irkutskogo gosudarstvennogo universiteta. seria matematika
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.411
H-Index - 3
eISSN - 2541-8785
pISSN - 1997-7670
DOI - 10.26516/1997-7670.2021.38.36
Subject(s) - mathematics , fractional calculus , degenerate energy levels , bounded function , mathematical analysis , operator (biology) , derivative (finance) , inverse , partial differential equation , term (time) , pure mathematics , physics , chemistry , biochemistry , geometry , repressor , quantum mechanics , transcription factor , financial economics , economics , gene
The issues of well-posedness of linear inverse coefficient problems for multi-term equations in Banach spaces with fractional Riemann – Liouville derivatives and with bounded operators at them are considered. Well-posedness criteria are obtained both for the equation resolved with respect to the highest fractional derivative, and in the case of a degenerate operator at the highest derivative in the equation. Two essentially different cases are investigated in the degenerate problem: when the fractional part of the order of the second-oldest derivative is equal to or different from the fractional part of the order of the highest fractional derivative. Abstract results are applied in the study of inverse problems for partial differential equations with polynomials from a self-adjoint elliptic differential operator with respect to spatial variables and with Riemann – Liouville derivatives in time.