Geodesic
Analytic in a sector resolving families of operators for degenerate evolution equations of a fractional order
Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 16 (2016) no. 2, pp. 93-107

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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. 
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     author = {V. E. Fedorov and E. A. Romanova and A. Debbouche},
     title = {Analytic in a sector resolving families of operators for degenerate evolution equations of a fractional order},
     journal = {Sibirskij \v{z}urnal \v{c}istoj i prikladnoj matematiki},
     pages = {93--107},
     publisher = {mathdoc},
     volume = {16},
     number = {2},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VNGU_2016_16_2_a8/}
}
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V. E. Fedorov; E. A. Romanova; A. Debbouche. Analytic in a sector resolving families of operators for degenerate evolution equations of a fractional order. Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 16 (2016) no. 2, pp. 93-107. http://geodesic.mathdoc.fr/item/VNGU_2016_16_2_a8/