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On the properties of a Cauchy-type problem for an abstract differential equation with fractional derivatives

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Abstract

We study the relationship between the solutions of abstract differential equations with fractional derivatives and their stability with respect to the perturbation by a bounded operator. Besides, we obtain representations for the solution of an inhomogeneous equation and for an equation containing a fractional power of the generator of a cosine operator function.

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Authors and Affiliations

  1. Belgorod State University, Russia

    A. V. Glushak

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  1. A. V. Glushak
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Correspondence to A. V. Glushak.

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Original Russian Text © A. V. Glushak, 2007, published in Matematicheskie Zametki, 2007, Vol. 82, No. 5, pp. 665–677.

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Glushak, A.V. On the properties of a Cauchy-type problem for an abstract differential equation with fractional derivatives. Math Notes 82, 596–607 (2007). https://doi.org/10.1134/S000143460711003X

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  • DOI: https://doi.org/10.1134/S000143460711003X

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