M. M. Kokurin, “The uniqueness of a solution to the inverse Cauchy problem for a fractional differential equation in a Banach space”, Izv. Vyssh. Uchebn. Zaved. Mat., 2013, no. 12, 19–35; Russian Math. (Iz. VUZ), 57:12 (2013), 16

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Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2013, Number 12, Pages 19–35 (Mi ivm8851)

This article is cited in 9 scientific papers (total in 9 papers)

The uniqueness of a solution to the inverse Cauchy problem for a fractional differential equation in a Banach space

M. M. Kokurin

Faculty of Physics and Mathematics, Mari State University, 1 Lenin sq., Ioshkar Ola, 424000 Russia

Full-text PDF (279 kB) Citations (9)

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Abstract: We consider linear fractional differential operator equations involving Caputo derivative. The goal of this paper is to establish conditions of the unique solvability of the inverse Cauchy problem for these equations. We use properties of the Mittag-Leffler function and the calculus of sectorial operators in a Banach space. For equations with operators in a general form we obtain sufficient conditions for the unique solvability, and for equations with densely defined sectorial operators we obtain necessary and sufficient unique solvability conditions.

Keywords: fractional differential equations, Caputo derivative, Banach space, inverse Cauchy problem, uniqueness of solution, ill-posed problems, Mittag-Leffler function, calculus of sectorial operators, fractional Fokker–Planck equation, subdiffusion.

Received: 31.07.2012

English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2013, Volume 57, Issue 12, Pages 16–30
DOI: https://doi.org/10.3103/S1066369X13120037

Bibliographic databases:

Document Type: Article

UDC: 517.983

Language: Russian

Citation: M. M. Kokurin, “The uniqueness of a solution to the inverse Cauchy problem for a fractional differential equation in a Banach space”, Izv. Vyssh. Uchebn. Zaved. Mat., 2013, no. 12, 19–35; Russian Math. (Iz. VUZ), 57:12 (2013), 16–30

Citation in format AMSBIB

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\by M.~M.~Kokurin

\paper The uniqueness of a~solution to the inverse Cauchy problem for a~fractional differential equation in a~Banach space

\jour Izv. Vyssh. Uchebn. Zaved. Mat.

\yr 2013

\issue 12

\pages 19--35

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\transl

\jour Russian Math. (Iz. VUZ)

\yr 2013

\vol 57

\issue 12

\pages 16--30

\crossref{https://doi.org/10.3103/S1066369X13120037}

\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84890469765}

Linking options:

https://www.mathnet.ru/eng/ivm8851

https://www.mathnet.ru/eng/ivm/y2013/i12/p19

This publication is cited in the following 9 articles:

M. M. Kokurin, “Discrete Approximation of Solutions of the Cauchy Problem for a Linear Homogeneous Differential-Operator Equation with a Caputo Fractional Derivative in a Banach Space”, J Math Sci, 272:6 (2023), 826
M. M. Kokurin, S. I. Piskarev, “A finite difference scheme on a graded mesh for solving Cauchy problems with a fractional Caputo derivative in a Banach space”, Russian Math. (Iz. VUZ), 66:11 (2022), 33–45
S. I. Piskarev, A. V. Ovchinnikov, “Attraktory, zatenenie i approksimatsiya abstraktnykh polulineinykh differentsialnykh uravnenii”, Funktsionalnyi analiz, Itogi nauki i tekhn. Sovrem. mat. i ee pril. Temat. obz., 189, VINITI RAN, M., 2021, 3–130
M. M. Kokurin, “Diskretnaya approksimatsiya reshenii zadachi Koshi dlya lineinogo odnorodnogo differentsialno-operatornogo uravneniya s drobnoi proizvodnoi Kaputo v banakhovom prostranstve”, Materialy XVII Vserossiiskoi molodezhnoi shkoly-konferentsii «Lobachevskie chteniya-2018», 23-28 noyabrya 2018 g., Kazan. Chast 1, Itogi nauki i tekhn. Sovrem. mat. i ee pril. Temat. obz., 175, VINITI RAN, M., 2020, 79–104
Yuan L., Cheng X., Liang K., “Solving a Backward Problem For a Distributed-Order Time Fractional Diffusion Equation By a New Adjoint Technique”, J. Inverse Ill-Posed Probl., 28:4 (2020), 471–488
Piskarev S., Siegmund S., “Approximations of Stable Manifolds in the Vicinity of Hyperbolic Equilibrium Points For Fractional Differential Equations”, Nonlinear Dyn., 95:1 (2019), 685–697
M. Yu. Kokurin, S. I. Piskarev, M. Spreafico, “Finite-Difference Methods for Fractional Differential Equations of Order $1/2$ ”, J. Math. Sci. (N. Y.), 230:6 (2018), 950–960
M. Slodicka, K. Siskova, “An inverse source problem in a semilinear time-fractional diffusion equation”, Comput. Math. Appl., 72:6 (2016), 1655–1669
Dmitry G. Orlovsky, “Parameter determination in a differential equation of fractional order with Riemann–Liouville fractional derivative in a Hilbert space”, Zhurn. SFU. Ser. Matem. i fiz., 8:1 (2015), 55–63

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

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Russian Mathematics (Izvestiya VUZ. Matematika)

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