|
Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2015, Number 1, Pages 71–83
(Mi ivm8966)
|
|
|
|
This article is cited in 40 scientific papers (total in 40 papers)
Resolving operators of degenerate evolution equations with fractional derivative with respect to time
V. E. Fedorov, D. M. Gordievskikh Chair of Mathematical Analysis, Chelyabinsk State University,
129 Br. Kashirinykh str., Chelyabinsk, 454001 Russia
Abstract:
We consider resolving operators of a fractional linear differential equation in a Banach space with a degenerate operator under the derivative. Under the assumption of relative $p$-boundedness of a pair of operators in this equation, we find the form of resolving operators and study their properties. It is shown that solution trajectories of the equation fill up a subspace of a Banach space. We obtain necessary and sufficient conditions for relative $p$-boundedness of a pair of operators in terms of families of resolving operators for degenerate fractional differential equation. Abstract results are illustrated by examples of the Cauchy problem for degenerate finite-dimensional system of fractional differential equations and of initial boundary-value problem for a fractional equation with respect to the time containing polynomials of Laplace operators with respect to spatial variables.
Keywords:
fractional differential equation, degenerate evolution equation, family of resolving operators, phase space, initial boundary value problem.
Received: 15.07.2013
Citation:
V. E. Fedorov, D. M. Gordievskikh, “Resolving operators of degenerate evolution equations with fractional derivative with respect to time”, Izv. Vyssh. Uchebn. Zaved. Mat., 2015, no. 1, 71–83; Russian Math. (Iz. VUZ), 59:1 (2015), 60–70
Linking options:
https://www.mathnet.ru/eng/ivm8966 https://www.mathnet.ru/eng/ivm/y2015/i1/p71
|
Statistics & downloads: |
Abstract page: | 338 | Full-text PDF : | 69 | References: | 50 | First page: | 29 |
|