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Mat. Zametki, 2007, Volume 82, Issue 5, Pages 665–677 (Mi mz4081)  

This article is cited in 5 scientific papers (total in 5 papers)

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

A. V. Glushak

Belgorod State University

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

DOI: https://doi.org/10.4213/mzm4081

Full text: PDF file (496 kB)
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English version:
Mathematical Notes, 2007, 82:5, 596–607

Bibliographic databases:

UDC: 517.983
Received: 09.02.2005
Revised: 10.04.2007

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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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Furati Kh.M., “A Cauchy-type problem with a sequential fractional derivative in the space of continuous functions”, Bound. Value Probl., 2012 (2012), 58, 14 pp.  crossref  mathscinet  zmath  isi  elib  scopus
    2. Furati Kh.M., “Bounds on the solution of a Cauchy-type problem involving a weighted sequential fractional derivative”, Fract. Calc. Appl. Anal., 16:1 (2013), 171–188  crossref  mathscinet  zmath  isi  elib  scopus
    3. Furati Kh.M., “A Cauchy-Type Problem Involving a Weighted Sequential Derivative in the Space of Integrable Functions”, Comput. Math. Appl., 66:5 (2013), 883–891  crossref  mathscinet  zmath  isi  elib  scopus
    4. Vijayakumar V., Selvakumar A., Murugesu R., “Controllability For a Class of Fractional Neutral Integro-Differential Equations With Unbounded Delay”, Appl. Math. Comput., 232 (2014), 303–312  crossref  mathscinet  zmath  isi  elib  scopus
    5. V. E. Fedorov, M. V. Plekhanova, R. R. Nazhimov, “Degenerate linear evolution equations with the Riemann–Liouville fractional derivative”, Siberian Math. J., 59:1 (2018), 136–146  mathnet  crossref  crossref  isi  elib
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