|
This article is cited in 3 scientific papers (total in 3 papers)
Mathematics
On solvability of some classes of equations with Hilfer derivative in Banach spaces
A. R. Volkovaa, V. E. Fedorova, D. M. Gordievskikhb a Chelyabinsk State University, Chelyabinsk, Russia
b Shadrinsk State Pedagogical University, Shadrinsk, Russia
Abstract:
The issues of unique solvability of a Cauchy-type problem for an evolutionary equation in a Banach space with a Hilfer fractional derivative and with a bounded operator are investigated. The existence of a unique solution to the problem is proved, the solution is presented using Mittag-Leffler operator functions. The abstract result is used when considering a class of initial boundary value problems for partial differential equations
Keywords:
Hilfer derivative, fractional order equation, initial problem, theorem on the existence and uniqueness of a solution, linear inhomogeneous equation, initial boundary value problem, Laplace operator.
Received: 22.10.2021 Revised: 16.12.2021
Citation:
A. R. Volkova, V. E. Fedorov, D. M. Gordievskikh, “On solvability of some classes of equations with Hilfer derivative in Banach spaces”, Chelyab. Fiz.-Mat. Zh., 7:1 (2022), 11–19
Linking options:
https://www.mathnet.ru/eng/chfmj267 https://www.mathnet.ru/eng/chfmj/v7/i1/p11
|
Statistics & downloads: |
Abstract page: | 176 | Full-text PDF : | 80 | References: | 36 |
|