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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
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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
\Bibitem{Orl15}
\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
\mathnet{http://mi.mathnet.ru/jsfu406}
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http://mi.mathnet.ru/eng/jsfu406 http://mi.mathnet.ru/eng/jsfu/v8/i1/p55
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V. E. Fedorov, N. D. Ivanova, “Identification problem for degenerate evolution equations of fractional order”, Fract. Calc. Appl. Anal., 20:3 (2017), 706–721
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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
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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
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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
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N. Kinash, J. Janno, “Inverse problems for a generalized subdiffusion equation with final overdetermination”, Math. Model. Anal., 24:2 (2019), 236–262
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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
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V. E. Fedorov, M. Kostic, “Identification problem for strongly degenerate evolution equations with the Gerasimov-Caputo derivative”, Differ. Equ., 56:12 (2020), 1613–1627
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M. Al Horani, M. Fabrizio, A. Favini, H. Tanabe, “Inverse problems for degenerate fractional integro-differential equations”, Mathematics, 8:4 (2020), 532
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