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Izv. Vyssh. Uchebn. Zaved. Mat., 2009, Number 9, Pages 13–24
(Mi ivm3062)
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This article is cited in 6 scientific papers (total in 6 papers)
Correctness of Cauchy-type problems for abstract differential equations with fractional derivatives
A. V. Glushak
Chair of Mathematical Analysis, Belgorod State University, Belgorod, Russia
Abstract:
We prove the uniform correctness of a Cauchy-type problem with two fractional derivatives and a bounded operator $A$. We propose a criterion for the uniform correctness of unbounded operator $A$.
Keywords:
equations of fractional order, uniform correctness of Cauchy-type problem, resolving operator.
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English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2009, 53:9, 10–19
Bibliographic databases:
 
UDC:
517.983
Received: 24.10.2006
Revised: 19.12.2008
Citation:
A. V. Glushak, “Correctness of Cauchy-type problems for abstract differential equations with fractional derivatives”, Izv. Vyssh. Uchebn. Zaved. Mat., 2009, no. 9, 13–24; Russian Math. (Iz. VUZ), 53:9 (2009), 10–19
Citation in format AMSBIB
\Bibitem{Glu09}
\by A.~V.~Glushak
\paper Correctness of Cauchy-type problems for abstract differential equations with fractional derivatives
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2009
\issue 9
\pages 13--24
\mathnet{http://mi.mathnet.ru/ivm3062}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2650571}
\zmath{https://zbmath.org/?q=an:1177.47090}
\transl
\jour Russian Math. (Iz. VUZ)
\yr 2009
\vol 53
\issue 9
\pages 10--19
\crossref{https://doi.org/10.3103/S1066369X09090023}
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This publication is cited in the following articles:
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Furati Kh.M., “A Cauchy-Type Problem with a Sequential Fractional Derivative in the Space of Continuous Functions”, Bound. Value Probl., 2012, 58
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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
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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
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Marina V. Plekhanova, “Degenerate distributed control systems with fractional time derivative”, Ural Math. J., 2:2 (2016), 58–71
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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
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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
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