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J. Sib. Fed. Univ. Math. Phys., 2015, Volume 8, Issue 1, Pages 55–63 (Mi jsfu406)  

This article is cited in 10 scientific papers (total in 10 papers)

Parameter determination in a differential equation of fractional order with Riemann–Liouville fractional derivative in a Hilbert space

Dmitry G. Orlovsky

National Research Nuclear University MEPhI, Kashirskoye shosse, 31, Moscow, 115409, Russia

Abstract: The Cauchy type problem for a differential equation with fractional derivative and self-adjoint operator in a Hilbert space is considered. The problem of parameter determination in equation by the value of the solution at a fixed point is presented. Theorems of existence and uniqueness of the solution are proved.

Keywords: equation of fractional order, Hilbert space, self-adjoint operator, Cauchy-type problem, Mittag–Leffler function, inverse problem, characteristic function.

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UDC: 517.986.7
Received: 10.10.2014
Received in revised form: 20.11.2014
Accepted: 15.12.2014

Citation: Dmitry G. Orlovsky, “Parameter determination in a differential equation of fractional order with Riemann–Liouville fractional derivative in a Hilbert space”, J. Sib. Fed. Univ. Math. Phys., 8:1 (2015), 55–63

Citation in format AMSBIB
\by Dmitry~G.~Orlovsky
\paper Parameter determination in a differential equation of fractional order with Riemann--Liouville fractional derivative in a Hilbert space
\jour J. Sib. Fed. Univ. Math. Phys.
\yr 2015
\vol 8
\issue 1
\pages 55--63

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    This publication is cited in the following articles:
    1. Fedorov V.E., Nagumanova A.V., Avilovich A.S., “a Class of Inverse Problems For Evolution Equations With the Riemann-Liouville Derivative in the Sectorial Case”, Math. Meth. Appl. Sci.  crossref  isi  scopus
    2. V. E. Fedorov, N. D. Ivanova, “Identification problem for degenerate evolution equations of fractional order”, Fract. Calc. Appl. Anal., 20:3 (2017), 706–721  crossref  mathscinet  zmath  isi  scopus
    3. V. E. Fedorov, A. V. Nagumanova, “Obratnaya zadacha dlya evolyutsionnogo uravneniya s drobnoi proizvodnoi Gerasimova–Kaputo v sektorialnom sluchae”, Izvestiya Irkutskogo gosudarstvennogo universiteta. Seriya Matematika, 28 (2019), 123–137  mathnet  crossref
    4. V. E. Fedorov, A. V. Nagumanova, “Lineinye obratnye zadachi dlya odnogo klassa vyrozhdennykh evolyutsionnykh uravnenii drobnogo poryadka”, Materialy IV Mezhdunarodnoi nauchnoi konferentsii “Aktualnye problemy prikladnoi matematiki”. Kabardino-Balkarskaya respublika, Nalchik, Prielbruse, 22–26 maya 2018 g. Chast III, Itogi nauki i tekhn. Ser. Sovrem. mat. i ee pril. Temat. obz., 167, VINITI RAN, M., 2019, 97–111  mathnet  crossref
    5. V. E. Fedorov, R. R. Nazhimov, “Inverse problems for a class of degenerate evolution equations with Riemann - Liouville derivative”, Fract. Calc. Appl. Anal., 22:2 (2019), 271–286  crossref  mathscinet  zmath  isi  scopus
    6. D. G. Orlovsky, “Determination of the parameter of the differential equation of fractional order with the Caputo derivative in Hilbert space”, Vii International Conference Problems of Mathematical Physics and Mathematical Modelling, Journal of Physics Conference Series, 1205, IOP Publishing Ltd, 2019, 012042  crossref  isi  scopus
    7. N. Kinash, J. Janno, “Inverse problems for a generalized subdiffusion equation with final overdetermination”, Math. Model. Anal., 24:2 (2019), 236–262  crossref  mathscinet  isi  scopus
    8. J. Janno, “Determination of time-dependent sources and parameters of nonlocal diffusion and wave equations from final data”, Fract. Calc. Appl. Anal., 23:6, SI (2020), 1678–1701  crossref  mathscinet  zmath  isi  scopus
    9. V. E. Fedorov, M. Kostic, “Identification problem for strongly degenerate evolution equations with the Gerasimov-Caputo derivative”, Differ. Equ., 56:12 (2020), 1613–1627  crossref  mathscinet  zmath  isi  scopus
    10. M. Al Horani, M. Fabrizio, A. Favini, H. Tanabe, “Inverse problems for degenerate fractional integro-differential equations”, Mathematics, 8:4 (2020), 532  crossref  mathscinet  isi  scopus
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