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Matematicheskie Zametki, 2007, Volume 82, Issue 5, Pages 665–677
DOI: https://doi.org/10.4213/mzm4081 (Mi mzm4081) 		 
This article is cited in 6 scientific papers (total in 6 papers)

On the Properties of a Cauchy-Type Problem for an Abstract Differential Equation with Fractional Derivatives

A. V. Glushak

Belgorod State University
Full-text PDF (496 kB) Citations (6)
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DOI: https://doi.org/10.4213/mzm4081
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.
Keywords: differential equation with fractional derivatives, Cauchy-type problem, Riemann–Liouville fractional derivative, fractional integral, Mittag-Leffler function.
Received: 09.02.2005
Revised: 10.04.2007
English version:
Mathematical Notes, 2007, Volume 82, Issue 5, Pages 596–607
DOI: https://doi.org/10.1134/S000143460711003X
Bibliographic databases:
UDC: 517.983
Language: Russian
Citation: A. V. Glushak, “On the Properties of a Cauchy-Type Problem for an Abstract Differential Equation with Fractional Derivatives”, Mat. Zametki, 82:5 (2007), 665–677; Math. Notes, 82:5 (2007), 596–607
Citation in format AMSBIB
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    • This publication is cited in the following 6 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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