Analytic Resolving Families for Equations with Distributed Riemann–Liouville Derivatives

Vladimir E. Fedorov, Wei-Shih Du, Marko Kostić and Aliya A. Abdrakhmanova
Additional contact information
Vladimir E. Fedorov: Department of Mathematical Analysis, Mathematics Faculty, Chelyabinsk State University, Kashirin Brothers Str. 129, 454001 Chelyabinsk, Russia
Wei-Shih Du: Department of Mathematics, National Kaohsiung Normal University, Kaohsiung 82444, Taiwan
Marko Kostić: Faculty of Technical Sciences, University of Novi Sad, Trg D. Obradovića 6, 21125 Novi Sad, Serbia
Aliya A. Abdrakhmanova: Department of Mathematics, Ufa State Aviation Technical University, Karl Marks Str. 12, 450077 Ufa, Russia

Mathematics, 2022, vol. 10, issue 5, 1-19

Abstract: Some new necessary and sufficient conditions for the existence of analytic resolving families of operators to the linear equation with a distributed Riemann–Liouville derivative in a Banach space are established. We study the unique solvability of a natural initial value problem with distributed fractional derivatives in the initial conditions to corresponding inhomogeneous equations. These abstract results are applied to a class of initial boundary value problems for equations with distributed derivatives in time and polynomials with respect to a self-adjoint elliptic differential operator in spatial variables.

Keywords: Riemann–Liouville derivative; distributed order equation; analytic resolving family of operators; generator of resolving family; perturbation theorem (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/10/5/681/pdf (application/pdf)
https://www.mdpi.com/2227-7390/10/5/681/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:10:y:2022:i:5:p:681-:d:755950

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().