Degenerate Linear Evolution Equations with the Riemann–Liouville Fractional Derivative
- Authors: Fedorov V.E.1, Plekhanova M.V.1, Nazhimov R.R.2
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Affiliations:
- Chelyabinsk State University South Ural State University
- Chelyabinsk State University
- Issue: Vol 59, No 1 (2018)
- Pages: 136-146
- Section: Article
- URL: https://journals.rcsi.science/0037-4466/article/view/171695
- DOI: https://doi.org/10.1134/S0037446618010159
- ID: 171695
Cite item
Abstract
We study the unique solvability of the Cauchy and Schowalter–Sidorov type problems in a Banach space for an evolution equation with a degenerate operator at the fractional derivative under the assumption that the operator acting on the unknown function in the equation is p-bounded with respect to the operator at the fractional derivative. The conditions are found ensuring existence of a unique solution representable by means of the Mittag-Leffler type functions. Some abstract results are illustrated by an example of a finite-dimensional degenerate system of equations of a fractional order and employed in the study of unique solvability of an initial-boundary value problem for the linearized Scott-Blair system of dynamics of a medium.
About the authors
V. E. Fedorov
Chelyabinsk State University South Ural State University
Author for correspondence.
Email: kar@csu.ru
Russian Federation, Chelyabinsk
M. V. Plekhanova
Chelyabinsk State University South Ural State University
Email: kar@csu.ru
Russian Federation, Chelyabinsk
R. R. Nazhimov
Chelyabinsk State University
Email: kar@csu.ru
Russian Federation, Chelyabinsk