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Matematicheskie Zametki, 2010, Volume 87, Issue 5, Pages 684–693
DOI: https://doi.org/10.4213/mzm4437
(Mi mzm4437)
 

This article is cited in 22 scientific papers (total in 22 papers)

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

A. V. Glushak

Belgorod State University
References:
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.
Received: 21.01.2008
English version:
Mathematical Notes, 2010, Volume 87, Issue 5, Pages 654–662
DOI: https://doi.org/10.1134/S0001434610050056
Bibliographic databases:
Document Type: Article
UDC: 517.983
Language: Russian
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
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Linking options:
  • https://www.mathnet.ru/eng/mzm4437
  • https://doi.org/10.4213/mzm4437
  • https://www.mathnet.ru/eng/mzm/v87/i5/p684
  • This publication is cited in the following 22 articles:
    1. Marina Plekhanova, Elizaveta Izhberdeeva, Darya Melekhina, Angelina Sagimbaeva, “GLOBAL SOLVABILITY OF NONLINEAR INVERSE PROBLEMS WITH DZHRBASHYAN–NERSESYAN DERIVATIVES AND SECTORIAL OPERATORS”, J Math Sci, 2025  crossref
    2. A. V. Nagumanova, V. E. Fedorov, “Pryamye i obratnye zadachi dlya lineinykh uravnenii s proizvodnoi Kaputo — Fabritsio i ogranichennym operatorom”, Chelyab. fiz.-matem. zhurn., 9:3 (2024), 389–406  mathnet  crossref
    3. V. E. Fedorov, A. V. Nagumanova, “Direct and Inverse Problems for Evolution Equations with Regular Integro-Differential Operators”, J Math Sci, 286:2 (2024), 278  crossref
    4. V. E. Fedorov, A. D. Godova, “Lineinye obratnye zadachi dlya integro-differentsialnykh uravnenii v banakhovykh prostranstvakh s ogranichennym operatorom”, Trudy Voronezhskoi zimnei matematicheskoi shkoly S. G. Kreina — 2024, SMFN, 70, no. 4, Rossiiskii universitet druzhby narodov, M., 2024, 679–690  mathnet  crossref
    5. Jie Mei, Miao Li, “Abstract fractional inverse source problem of order 0<\alpha <1 in a Banach space”, Fract Calc Appl Anal, 26:1 (2023), 276  crossref
    6. K. V. Boiko, V. E. Fedorov, “Obratnaya zadacha dlya odnogo klassa vyrozhdennykh evolyutsionnykh uravnenii s neskolkimi proizvodnymi Gerasimova—Kaputo”, Geometriya, mekhanika i differentsialnye uravneniya, Itogi nauki i tekhn. Sovrem. mat. i ee pril. Temat. obz., 213, VINITI RAN, M., 2022, 38–46  mathnet  crossref
    7. M. V. Plekhanova, E. M. Izhberdeeva, “O korrektnosti obratnoi zadachi dlya vyrozhdennogo evolyutsionnogo uravneniya s drobnoi proizvodnoi Dzhrbashyana—Nersesyana”, Geometriya, mekhanika i differentsialnye uravneniya, Itogi nauki i tekhn. Sovrem. mat. i ee pril. Temat. obz., 213, VINITI RAN, M., 2022, 80–88  mathnet  crossref
    8. V. E. Fedorov, A. V. Nagumanova, “Inverse Linear Problems for a Certain Class of Degenerate Fractional Evolution Equations”, J Math Sci, 260:3 (2022), 371  crossref
    9. 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., 44:15 (2021), 11961–11969  crossref  mathscinet  isi
    10. M. M. Turov, V. E. Fedorov, B. T. Kien, “Linear inverse problems for multi-term equations with Riemann — Liouville derivatives”, Izvestiya Irkutskogo gosudarstvennogo universiteta. Seriya Matematika, 38 (2021), 36–53  mathnet  crossref
    11. Fedorov V.E., Nagumanova V A., Kostic M., “A Class of Inverse Problems For Fractional Order Degenerate Evolution Equations”, J. Inverse Ill-Posed Probl., 29:2 (2021), 173–184  crossref  mathscinet  isi
    12. Kostin A.B., Piskarev I S., “Inverse Source Problem For the Abstract Fractional Differential Equation”, J. Inverse Ill-Posed Probl., 29:2 (2021), 267–281  crossref  mathscinet  isi
    13. 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
    14. 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  scopus
    15. 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
    16. 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  mathscinet  isi  scopus
    17. 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
    18. 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. Sovrem. mat. i ee pril. Temat. obz., 167, VINITI RAN, M., 2019, 97–111  mathnet  crossref
    19. 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
    20. 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
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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