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 to 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.
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Original Russian Text © V.E. Fedorov, D.M. Gordievskikh, 2015, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2015, No. 1, pp. 71–83.
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Fedorov, V.E., Gordievskikh, D.M. Resolving operators of degenerate evolution equations with fractional derivative with respect to time. Russ Math. 59, 60–70 (2015). https://doi.org/10.3103/S1066369X15010065
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DOI: https://doi.org/10.3103/S1066369X15010065