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

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Matematicheskie Zametki, 2005, Volume 77, Issue 1, Pages 28–41
DOI: https://doi.org/10.4213/mzm2466 (Mi mzm2466)

This article is cited in 12 scientific papers (total in 12 papers)

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

A. V. Glushak

Voronezh State Technical University

Full-text PDF (230 kB) Citations (12)

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

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.

Received: 05.07.2002
Revised: 24.02.2004

English version:
Mathematical Notes, 2005, Volume 77, Issue 1, Pages 26–38
DOI: https://doi.org/10.1007/s11006-005-0003-5

Bibliographic databases:

UDC: 517.983

Language: Russian

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

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Linking options:

https://www.mathnet.ru/eng/mzm2466

https://doi.org/10.4213/mzm2466

https://www.mathnet.ru/eng/mzm/v77/i1/p28

This publication is cited in the following 12 articles:

Vladimir E. Fedorov, Dar'ya A. Vershinina, “Strongly Continuous Resolving Families of Equations with Riemann–Liouville Derivative”, J Math Sci, 2025
K. V. Boiko, V. E. Fedorov, “Obratnaya zadacha dlya odnogo klassa vyrozhdennykh evolyutsionnykh uravnenii s neskolkimi proizvodnymi Gerasimova—Kaputo”, Geometriya, mekhanika i differentsialnye uravneniya, Itogi nauki i tekhn. Sovrem. mat. i ee pril. Temat. obz., 213, VINITI RAN, M., 2022, 38–46
V. E. Fedorov, M. M. Turov, “The defect of a Cauchy type problem for linear equations with several Riemann–Liouville derivatives”, Siberian Math. J., 62:5 (2021), 925–942
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
Abstract Volterra Integro-Differential Equations, 2015, 431
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
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
Umarov S., “On Fractional Duhamel's Principle and its Applications”, J. Differ. Equ., 252:10 (2012), 5217–5234
Furati Kh.M., “A Cauchy-Type Problem with a Sequential Fractional Derivative in the Space of Continuous Functions”, Bound. Value Probl., 2012, 58
Kh. K. Avad, A. V. Glushak, “Perturbation of an abstract differential equation containing fractional Riemann-Liouville derivatives”, Diff Equat, 46:6 (2010), 867
A. V. Glushak, “Correctness of Cauchy-type problems for abstract differential equations with fractional derivatives”, Russian Math. (Iz. VUZ), 53:9 (2009), 10–19
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

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

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