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.
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
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\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
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\crossref{https://doi.org/10.4213/mzm4437}
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\jour Math. Notes
\yr 2010
\vol 87
\issue 5
\pages 654--662
\crossref{https://doi.org/10.1134/S0001434610050056}
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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
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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
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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
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Al Horani M., Fabrizio M., Favini A., Tanabe H., “Inverse Problems For Degenerate Fractional Integro-Differential Equations”, Mathematics, 8:4 (2020), 532
Fedorov V.E., Kostic M., “Identification Problem For Strongly Degenerate Evolution Equations With the Gerasimov-Caputo Derivative”, Differ. Equ., 56:12 (2020), 1613–1627
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
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