RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PERSONAL OFFICE
General information
Latest issue
Archive
Impact factor

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki:
Year:
Volume:
Issue:
Page:
Find






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


Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2017, Volume 27, Issue 4, Pages 515–531 (Mi vuu605)  

MATHEMATICS

Approximation of ordinary fractional differential equations by differential equations with a small parameter

S. Yu. Lukashchuk

Ufa State Aviation Technical University, ul. K. Marksa, 12, Ufa, 450008, Russia

Abstract: An approach to approximation of ordinary fractional differential equations by integer-order differential equations is proposed. It is assumed that the order of fractional differentiation is close to integer. Perturbation expansions for the Riemann–Liouville and Caputo fractional derivatives are derived in terms of a suitable small parameter extracted from the order of fractional differentiation. The first-order term of these expansions is represented by series depending on integer-order derivatives of all integer orders. The expansions obtained permit one to approximate ordinary fractional differential equations, involving such types of fractional derivatives, by integer-order differential equations with a small parameter. It is proved that, for fractional differential equations belonging to a certain class, corresponding approximate equations contain only a finite number of integer-order derivatives. Approximate solutions to such equations can be obtained using well-known perturbation techniques. The proposed approach is illustrated by several examples.

Keywords: ordinary fractional differential equation, small parameter, approximation, approximate solution.

Funding Agency Grant Number
Ministry of Education and Science of the Russian Federation 1.3103.2017/4.6


DOI: https://doi.org/10.20537/vm170403

Full text: PDF file (337 kB)
References: PDF file   HTML file

Document Type: Article
UDC: 517.928
MSC: 34A08, 34E10
Received: 21.08.2017

Citation: S. Yu. Lukashchuk, “Approximation of ordinary fractional differential equations by differential equations with a small parameter”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 27:4 (2017), 515–531

Citation in format AMSBIB
\Bibitem{Luk17}
\by S.~Yu.~Lukashchuk
\paper Approximation of ordinary fractional differential equations by differential equations with a small parameter
\jour Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki
\yr 2017
\vol 27
\issue 4
\pages 515--531
\mathnet{http://mi.mathnet.ru/vuu605}
\crossref{https://doi.org/10.20537/vm170403}
\elib{http://elibrary.ru/item.asp?id=32248454}


Linking options:
  • http://mi.mathnet.ru/eng/vuu605
  • http://mi.mathnet.ru/eng/vuu/v27/i4/p515

    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
  • Вестник Удмуртского университета. Математика. Механика. Компьютерные науки
    Number of views:
    This page:133
    Full text:61
    References:22

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