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Mat. Zametki, 2010, Volume 87, Issue 5, Pages 684–693 (Mi mz4437)  

This article is cited in 11 scientific papers (total in 11 papers)

On an Inverse Problem for an Abstract Differential Equation of Fractional Order

A. V. Glushak

Belgorod State University

Abstract: In Banach space, we consider the problem of determining the solution and a summand of a differential equation of fractional order from the initial and redundant conditions containing fractional Riemann–Liouville integrals. It is shown that the solvability of the problem under consideration depends on the distribution of zeros of the Mittag–Leffler function.

Keywords: differential equation of fractional order, Riemann–Liouville integral, densely defined linear operator, Mittag–Leffler function, Cesàro mean, Banach space


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English version:
Mathematical Notes, 2010, 87:5, 654–662

Bibliographic databases:

UDC: 517.983
Received: 21.01.2008

Citation: A. V. Glushak, “On an Inverse Problem for an Abstract Differential Equation of Fractional Order”, Mat. Zametki, 87:5 (2010), 684–693; Math. Notes, 87:5 (2010), 654–662

Citation in format AMSBIB
\by A.~V.~Glushak
\paper On an Inverse Problem for an Abstract Differential Equation of Fractional Order
\jour Mat. Zametki
\yr 2010
\vol 87
\issue 5
\pages 684--693
\jour Math. Notes
\yr 2010
\vol 87
\issue 5
\pages 654--662

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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
    2. M. M. Kokurin, “The uniqueness of a solution to the inverse Cauchy problem for a fractional differential equation in a Banach space”, Russian Math. (Iz. VUZ), 57:12 (2013), 16–30  mathnet  crossref
    3. Malik S.A., Aziz S., “An Inverse Source Problem For a Two Parameter Anomalous Diffusion Equation With Nonlocal Boundary Conditions”, Comput. Math. Appl., 73:12 (2017), 2548–2560  crossref  mathscinet  zmath  isi  scopus
    4. Fedorov V.E., Ivanova N.D., “Identification Problem For Degenerate Evolution Equations of Fractional Order”, Fract. Calc. Appl. Anal., 20:3 (2017), 706–721  crossref  mathscinet  zmath  isi  scopus
    5. Glushak A.V., Nekrasova I.V., Florinsky V.V., Yaduta A.Z., “Direct and Inverse Problem of Cauchy Type For the Fraction Equation With the Degeneration and Non-Loaded Operator Coefficient”, Dilemas Contemp.-Educ. Politica Valores, 6:SI (2019), 66  isi
    6. Fedorov V.E., Nazhimov R.R., “Inverse Problems For a Class of Degenerate Evolution Equations With Riemann - Liouville Derivative”, Fract. Calc. Appl. Anal., 22:2 (2019), 271–286  crossref  isi
    7. 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
    8. 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
    9. Ahmad B., Alghanmi M., Alsaedi A., Ntouyas S.K., “Multi-Term Fractional Differential Equations With Generalized Integral Boundary Conditions”, Fractal Pract., 3:3 (2019), UNSP 44  crossref  mathscinet  isi
    10. Al Horani M., Fabrizio M., Favini A., Tanabe H., “Inverse Problems For Degenerate Fractional Integro-Differential Equations”, Mathematics, 8:4 (2020), 532  crossref  mathscinet  isi
    11. Fedorov V.E., Kostic M., “Identification Problem For Strongly Degenerate Evolution Equations With the Gerasimov-Caputo Derivative”, Differ. Equ., 56:12 (2020), 1613–1627  crossref  mathscinet  isi
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