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 Mat. Zametki, 2005, Volume 77, Issue 1, Pages 28–41 (Mi mz2466)

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

A. V. Glushak

Voronezh State Technical University

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.

DOI: https://doi.org/10.4213/mzm2466

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English version:
Mathematical Notes, 2005, 77:1, 26–38

Bibliographic databases:

UDC: 517.983
Revised: 24.02.2004

Citation: A. V. Glushak, “Cauchy-type problem for an abstract differential equation with fractional derivatives”, Mat. Zametki, 77:1 (2005), 28–41; Math. Notes, 77:1 (2005), 26–38

Citation in format AMSBIB
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• http://mi.mathnet.ru/eng/mz2466
• https://doi.org/10.4213/mzm2466
• http://mi.mathnet.ru/eng/mz/v77/i1/p28

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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. A. V. Glushak, “On the Properties of a Cauchy-Type Problem for an Abstract Differential Equation with Fractional Derivatives”, Math. Notes, 82:5 (2007), 596–607
2. A. V. Glushak, “Correctness of Cauchy-type problems for abstract differential equations with fractional derivatives”, Russian Math. (Iz. VUZ), 53:9 (2009), 10–19
3. Umarov S., “On Fractional Duhamel's Principle and its Applications”, J. Differ. Equ., 252:10 (2012), 5217–5234
4. Furati Kh.M., “A Cauchy-Type Problem with a Sequential Fractional Derivative in the Space of Continuous Functions”, Bound. Value Probl., 2012, 58
5. Furati Kh.M., “Bounds on the Solution of a Cauchy-Type Problem Involving a Weighted Sequential Fractional Derivative”, Fract. Calc. Appl. Anal., 16:1, SI (2013), 171–188
6. 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
7. V. V. Katrakhov, S. M. Sitnik, “Metod operatorov preobrazovaniya i kraevye zadachi dlya singulyarnykh ellipticheskikh uravnenii”, Singulyarnye differentsialnye uravneniya, SMFN, 64, no. 2, Rossiiskii universitet druzhby narodov, M., 2018, 211–426
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