RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PERSONAL OFFICE
General information
Latest issue
Archive
Impact factor
Subscription
Guidelines for authors
License agreement
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



TMF:
Year:
Volume:
Issue:
Page:
Find






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


TMF, 2015, Volume 184, Number 2, Pages 179–199 (Mi tmf8833)  

This article is cited in 6 scientific papers (total in 6 papers)

Constructing conservation laws for fractional-order integro-differential equations

S. Yu. Lukashchuk

Ufa State Aviation Technical University, Ufa, Russia

Abstract: In a class of functions depending on linear integro-differential fractional-order variables, we prove an analogue of the fundamental operator identity relating the infinitesimal operator of a point transformation group, the Euler–Lagrange differential operator, and Noether operators. Using this identity, we prove fractional-differential analogues of the Noether theorem and its generalizations applicable to equations with fractional-order integrals and derivatives of various types that are Euler–Lagrange equations. In explicit form, we give fractional-differential generalizations of Noether operators that gives an efficient way to construct conservation laws, which we illustrate with three examples.

Keywords: integro-differential fractional-order equation, symmetry, conservation law, fundamental operator identity, Noether theorem

Funding Agency Grant Number
Ministry of Education and Science of the Russian Federation 11.G34.31.0042


DOI: https://doi.org/10.4213/tmf8833

Full text: PDF file (500 kB)
References: PDF file   HTML file

English version:
Theoretical and Mathematical Physics, 2015, 184:2, 1049–1066

Bibliographic databases:

PACS: 11.10.Lm, 11.30.-j
MSC: 45K05, 70S10, 70G65
Received: 03.12.2014
Revised: 03.03.2015

Citation: S. Yu. Lukashchuk, “Constructing conservation laws for fractional-order integro-differential equations”, TMF, 184:2 (2015), 179–199; Theoret. and Math. Phys., 184:2 (2015), 1049–1066

Citation in format AMSBIB
\Bibitem{Luk15}
\by S.~Yu.~Lukashchuk
\paper Constructing conservation laws for fractional-order integro-differential equations
\jour TMF
\yr 2015
\vol 184
\issue 2
\pages 179--199
\mathnet{http://mi.mathnet.ru/tmf8833}
\crossref{https://doi.org/10.4213/tmf8833}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3399674}
\adsnasa{http://adsabs.harvard.edu/cgi-bin/bib_query?2015TMP...184.1049L}
\elib{http://elibrary.ru/item.asp?id=24073860}
\transl
\jour Theoret. and Math. Phys.
\yr 2015
\vol 184
\issue 2
\pages 1049--1066
\crossref{https://doi.org/10.1007/s11232-015-0317-8}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000361532600001}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84942133729}


Linking options:
  • http://mi.mathnet.ru/eng/tmf8833
  • https://doi.org/10.4213/tmf8833
  • http://mi.mathnet.ru/eng/tmf/v184/i2/p179

    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. S. Yu. Lukashchuk, “Symmetry reduction and invariant solutions for nonlinear fractional diffusion equation with a source term”, Ufa Math. J., 8:4 (2016), 111–122  mathnet  crossref  isi  elib
    2. D.-W. Ding, J. Yan, N. Wang, D. Liang, “Adaptive synchronization of fractional order complex-variable dynamical networks via pinning control”, Commun. Theor. Phys., 68:3 (2017), 366–374  crossref  zmath  isi  scopus
    3. M. Pan, L. Zheng, Ch. Liu, F. Liu, “Symmetry analysis and conservation laws to the space-fractional Prandtl equation”, Nonlinear Dyn., 90:2 (2017), 1343–1351  crossref  mathscinet  zmath  isi  scopus
    4. S. Yu. Lukashchuk, R. D. Saburova, “Approximate symmetry group classification for a nonlinear fractional filtration equation of diffusion-wave type”, Nonlinear Dyn., 93:2 (2018), 295–305  crossref  isi  scopus
    5. Lukashchuk S.Yu., “Approximate Conservation Laws For Fractional Differential Equations”, Commun. Nonlinear Sci. Numer. Simul., 68 (2019), 147–159  crossref  mathscinet  isi  scopus
    6. Habibi N., Lashkarian E., Dastranj E., Hejazi S.R., “Lie Symmetry Analysis, Conservation Laws and Numerical Approximations of Time-Fractional Fokker-Planck Equations For Special Stochastic Process in Foreign Exchange Markets”, Physica A, 513 (2019), 750–766  crossref  mathscinet  isi  scopus
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
    Number of views:
    This page:233
    Full text:10
    References:43
    First page:64

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2019