|
This article is cited in 25 scientific papers (total in 25 papers)
Analytic in a sector resolving families of operators for degenerate evolution equations of a fractional order
V. E. Fedorova, E. A. Romanovaa, A. Debboucheb a Chelyabinsk State University
b Université 8 Mai 1945 - Guelma
Abstract:
We introduce a class of operator pairs for linear homogeneous fractional differential equations in Banach spaces. Reflexive Banach space was decomposed into direct sum of the phase
space of the equation and of the kernel of the operator under the fractional derivative. Analytic in a sector of the complex plane containing the positive semiaxis family of resolving
operators is constructed. It degenerates only on the kernel of the operator at the derivative.
Work results generalize the analogous assertions on weakly degenerate analytic resolving
semigroups for the case of degenerate equations of arbitrary fractional order. They are applied to the research of initial boundary value problems for a class of partial differential
equations with fractional time derivative that contain polynomials of Laplace operator with
respect to spatial variables.
Keywords:
fractional differential equation, degenerate evolution equation, phase space, analytic family of resolving operators, initial boundary value problem.
Received: 26.12.2015
Citation:
V. E. Fedorov, E. A. Romanova, A. Debbouche, “Analytic in a sector resolving families of operators for degenerate evolution equations of a fractional order”, Sib. J. Pure and Appl. Math., 16:2 (2016), 93–107; J. Math. Sci., 228:4 (2018), 380–394
Linking options:
https://www.mathnet.ru/eng/vngu405 https://www.mathnet.ru/eng/vngu/v16/i2/p93
|
Statistics & downloads: |
Abstract page: | 4539 | Full-text PDF : | 59 | References: | 42 | First page: | 33 |
|