Home Mathematics On an inverse spectral problem for one integro-differential operator of fractional order
Article
Licensed
Unlicensed Requires Authentication

On an inverse spectral problem for one integro-differential operator of fractional order

  • Mikhail Ignatiev ORCID logo EMAIL logo
Published/Copyright: March 28, 2018

Abstract

An inverse spectral problem for some integro-differential operator of fractional order α(1,2) is studied. We show that the specification of the spectrum together with a certain a priori information about the structure of the operator determines such operator uniquely. The proof is constructive and provides a procedure for solving the inverse problem.

Award Identifier / Grant number: 17-11-01193

Funding statement: This work was supported by the Russian Science Foundation (project no. 17-11-01193).

References

[1] S. A. Buterin, The inverse problem of recovering the Volterra convolution operator from the incomplete spectrum of its rank-one perturbation, Inverse Problems 22 (2006), 2223–2236. 10.1088/0266-5611/22/6/019Search in Google Scholar

[2] S. A. Buterin, On an inverse spectral problem for a convolution integro-differential operator, Results Math. 50 (2007), no. 3–4, 173–181. 10.1007/s00025-007-0244-6Search in Google Scholar

[3] S. A. Buterin, On the reconstruction of a convolution perturbation of the Sturm–Liouville operator from the spectrum, Differential Equations 46 (2010), no. 1, 150–154. 10.1134/S0012266110010167Search in Google Scholar

[4] M. S. Eremin, Inverse problem for second-order integro-differential equation with a singularity, Differ. Uravn. 24 (1988), no. 2, 350–351. Search in Google Scholar

[5] M. Y. Ignat’ev, On the similarity between Volterra operators and transformation operators for integro-differential operators of fractional order, Math. Notes 73 (2003), no. 2, 192–201. 10.1023/A:1022154908077Search in Google Scholar

[6] Y. V. Kuryshova, The inverse spectral problem for integro-differential operators, Mat. Zametki 81 (2007), no. 6, 855–866. 10.1134/S0001434607050240Search in Google Scholar

[7] M. M. Malamud, On some inverse problems, Boundary Value Problems of Mathematical Physics, “Nauka”, Kiev (1979), 116–124. Search in Google Scholar

[8] M. M. Malamud, Similar Volterra operators and related aspects of the theory of fractional differential equations, Tr. Mosk. Mat. Obs. 55 (1993), 73–148. Search in Google Scholar

[9] V. M. Martirosyan, Integral transformations with kernels of Mittag-Leffler type in the classes Lp(0,+), 1<p2, Math. USSR Sb. 57 (1987), no. 1, 97–109. 10.1070/SM1987v057n01ABEH003057Search in Google Scholar

[10] A. Y. Popov and A. M. Sedletskii, Distribution of roots of Mittag-Leffler functions, J. Math. Sci. (N. Y.) 190 (2013), no. 2, 209–409. 10.1007/s10958-013-1255-3Search in Google Scholar

[11] V. A. Yurko, An inverse problem for integral operators, Math. Notes 37 (1985), 378–385. 10.1007/BF01157969Search in Google Scholar

[12] V. A. Yurko, Inverse problem for integro-differential operators, Mat. Zametki 50 (1991), no. 5, 134–144. 10.1201/9781482287431-19Search in Google Scholar

Received: 2017-12-22
Accepted: 2018-03-03
Published Online: 2018-03-28
Published in Print: 2019-02-01

© 2019 Walter de Gruyter GmbH, Berlin/Boston

Downloaded on 13.2.2026 from https://www.degruyterbrill.com/document/doi/10.1515/jiip-2017-0121/html
Scroll to top button