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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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  • https://doi.org/10.4213/mzm4081
  • https://www.mathnet.ru/eng/mzm/v82/i5/p665
    • This publication is cited in the following 6 articles:
    1. V. E. Fedorov, A. S. Avilovich, “A Cauchy type problem for a degenerate equation with the Riemann–Liouville derivative in the sectorial case”, Siberian Math. J., 60:2 (2019), 359–372  mathnet  crossref  crossref  isi  elib
    2. 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
    3. 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
    4. 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
    5. 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
    6. 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
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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