Geodesic
Resolving operators of degenerate evolution equations with fractional derivative with respect to time
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 1 (2015), pp. 71-83

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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. 
@article{IVM_2015_1_a5,
     author = {V. E. Fedorov and D. M. Gordievskikh},
     title = {Resolving operators of degenerate evolution equations with fractional derivative with respect to time},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {71--83},
     publisher = {mathdoc},
     number = {1},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2015_1_a5/}
}
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V. E. Fedorov; D. M. Gordievskikh. Resolving operators of degenerate evolution equations with fractional derivative with respect to time. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 1 (2015), pp. 71-83. http://geodesic.mathdoc.fr/item/IVM_2015_1_a5/