RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
General information
Latest issue
Archive
Impact factor
Journal history

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Fundam. Prikl. Mat.:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Fundam. Prikl. Mat., 2006, Volume 12, Issue 6, Pages 137–155 (Mi fpm994)  

This article is cited in 8 scientific papers (total in 8 papers)

On the number of real eigenvalues of a certain boundary-value problem for a second-order equation with fractional derivative

A. Yu. Popov

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Abstract: The asymptotics as $\alpha\to0+$ of the number of real eigenvalues $\lambda_n(\alpha)$ of the problem $y"(x)+\lambda D_{0}^{\alpha}y(x)=0$, $0<x<1$, $y(0)=y(1)=0$, is found. The minimization of real eigenvalues was carried out. It is proved that $\lim\limits_{\alpha\to0+}\lambda_n(\alpha)=(\pi n)^2$.

Full text: PDF file (205 kB)
References: PDF file   HTML file

English version:
Journal of Mathematical Sciences (New York), 2008, 151:1, 2726–2740

Bibliographic databases:

UDC: 517.589+517.927.2

Citation: A. Yu. Popov, “On the number of real eigenvalues of a certain boundary-value problem for a second-order equation with fractional derivative”, Fundam. Prikl. Mat., 12:6 (2006), 137–155; J. Math. Sci., 151:1 (2008), 2726–2740

Citation in format AMSBIB
\Bibitem{Pop06}
\by A.~Yu.~Popov
\paper On the number of real eigenvalues of a~certain boundary-value problem for a~second-order equation with fractional derivative
\jour Fundam. Prikl. Mat.
\yr 2006
\vol 12
\issue 6
\pages 137--155
\mathnet{http://mi.mathnet.ru/fpm994}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2314136}
\zmath{https://zbmath.org/?q=an:1151.34320}
\transl
\jour J. Math. Sci.
\yr 2008
\vol 151
\issue 1
\pages 2726--2740
\crossref{https://doi.org/10.1007/s10948-008-0169-7}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-42449160660}


Linking options:
  • http://mi.mathnet.ru/eng/fpm994
  • http://mi.mathnet.ru/eng/fpm/v12/i6/p137

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. A. Yu. Popov, A. M. Sedletskii, “Distribution of roots of Mittag-Leffler functions”, Journal of Mathematical Sciences, 190:2 (2013), 209–409  mathnet  crossref  mathscinet  zmath
    2. Nakhusheva Z.A., “On a nonlocal boundary value problem for a degenerating second-order hyperbolic equation with a spectral parameter”, Differ. Equ., 47:10 (2011), 1468–1481  crossref  mathscinet  zmath  isi  elib  elib
    3. T. S. Aleroev, “Kraevye zadachi dlya differentsialnykh uravnenii drobnogo poryadka”, Sib. elektron. matem. izv., 10 (2013), 41–55  mathnet
    4. T. S. Aleroev, E. M. Zveryaev, E. A. Larionov, “Drobnoe ischislenie i ego primenenie”, Preprinty IPM im. M. V. Keldysha, 2013, 037, 26 pp.  mathnet
    5. Masaeva O.Kh., “Dirichlet Problem for a Nonlocal Wave Equation”, Differ. Equ., 49:12 (2013), 1518–1523  crossref  mathscinet  zmath  isi  elib
    6. B. I. Efendiev, “Dirichlet Problem for Second-Order Ordinary Differential Equations with Segment-Order Derivative”, Math. Notes, 97:4 (2015), 632–640  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    7. O. Kh. Masaeva, “Necessary and sufficient conditions for the uniqueness of the Dirichlet problem for nonlocal wave equation”, Bulletin KRASEC. Phys. & Math. Sci., 11:2 (2015), 19–23  mathnet  crossref  crossref  elib
    8. N. E. Tokmagambetov, B. T. Torebek, “Symmetric differential operators of fractional order and their extensions”, Trans. Moscow Math. Soc., 2018, 177–185  mathnet  crossref  elib
  • Фундаментальная и прикладная математика
    Number of views:
    This page:371
    Full text:125
    References:40

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2020