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Cauchy-type problem for an abstract differential equation with fractional derivatives

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Abstract

The uniform well-posedness of a Cauchy-type problem with two fractional derivatives and bounded operator A is proved. For an unbounded operator A we present a test for the uniform well-posedness of the problem under consideration consistent with the test for the uniform well-posedness of the Cauchy problem for an equation of second order.

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Translated from Matematicheskie Zametki, vol. 77, no. 1, 2005, pp. 28–41.

Original Russian Text Copyright © 2005 by A. V. Glushak.

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Glushak, A.V. Cauchy-type problem for an abstract differential equation with fractional derivatives. Math Notes 77, 26–38 (2005). https://doi.org/10.1007/s11006-005-0003-5

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  • DOI: https://doi.org/10.1007/s11006-005-0003-5

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