l-problem of moments for one-dimensional integro-differential equations with Erdélyi-Kober operators

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Abstract

Purpose: to investigate the possibility of statement of l-problem of moments for one-dimensional linear equations of three types, which contain Erdélyi-Kober differential and integral operators of fractional order.

Methods: formulation of l-problem of moments for each type of investigated equations, analytical investigation and solution of problem formulated

Results. Conditions derived that determine the possibility and solvability of the problem stated. In some cases an explicit solutions of l-problem of moments obtained.

Conclusions. The possibility of statement of formulated l-problem of moments shown in cases that defined by conditions obtained in paper. Some analytical solutions of investigated problem obtained.

About the authors

Sergey S. Postnov

V. A. Trapeznikov Institute of Control Sciences of Russian Academy of Sciences

Author for correspondence.
Email: postnov.sergey@inbox.ru
ORCID iD: 0000-0002-0392-3762
SPIN-code: 2778-4826
Russian Federation, 65, Profsoyuznaya Street, Moscow, 117997

References

  1. Agrawal O.P. // Nonlin. Dyn. - 2004. - Vol. 38. - P. 323-337.
  2. Frederico G.S.F., Torres D.F.M. // Int. Math. Forum. - 2008. - Vol. 3 (10). - P. 479-493.
  3. Кубышкин В.А., Постнов С.С. // Автоматика и телемеханика - 2014 - № 5. - С. 3-17.
  4. Kamocki R. // Math. Meth. Appl. Sci. - 2014. - Vol. 37 (11). - P. 1668-1686.
  5. Kamocki R., Majewski M. // Optimal Control Appl. Meth. - 2014. - Vol. 36, issue 4. - doi: 10.1002/oca.2150.
  6. Kilbas A.A., Srivastava H.M., Trujillo J.J. Theory and applications of fractional differential equations. - Amsterdam: Elsevier, 2006. - 541 p.
  7. Kiryakova V. Generalized Fractional Calculus and Applications. - Harlow, New York: Longman & J. Wiley, 1994. - 388 p.
  8. Plociniczak L. // SIAM J. Appl. Math. - 2014. - Vol. 74, No. 4. - P. 1219-1237.
  9. Sneddon I.N. // Lecture Notes in Math. - 1975. - Vol. 457. - P. 37-79.
  10. Kiryakova V. // AIP Conf. Proc. - 2011. - Vol. 1410. - P. 247-258.
  11. Крейн М.Г., Нудельман А.А. Проблема моментов Маркова и экстремальные задачи. - М.: Наука, 1973. - 552 с.
  12. Concezzi M., Garra R., Spigler R. // Fract. Calc. Appl. Anal. - 2015. - Vol. 18, No 5. - P. 1212-1231.
  13. Luchko Yu., Trujillo J.J. // Fract. Calc. Appl. Anal. - 2007. - Vol. 10. - P. 249-267.
  14. Бутковский А.Г. Методы управления системами с распределёнными параметрами. - М.: Наука, 1975. - 568 с.
  15. Kubyshkin V.A., Postnov S.S. // J. of Control Science and Engineering. - 2016. - Vol. 2016. - Article ID 4873083 (12 pages).

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