IDEAS home Printed from https://ideas.repec.org/a/spr/scient/v98y2014i1d10.1007_s11192-013-1032-6.html
   My bibliography  Save this article

On development of fractional calculus during the last fifty years

Author

Listed:
  • J. A. Tenreiro Machado

    (Institute of Engineering, Polytechnic of Porto)

  • Alexandra M. S. F. Galhano

    (Institute of Engineering, Polytechnic of Porto)

  • Juan J. Trujillo

    (Universidad de La Laguna)

Abstract

Fractional calculus generalizes integer order derivatives and integrals. During the last half century a considerable progress took place in this scientific area. This paper addresses the evolution and establishes an assertive measure of the research development.

Suggested Citation

  • J. A. Tenreiro Machado & Alexandra M. S. F. Galhano & Juan J. Trujillo, 2014. "On development of fractional calculus during the last fifty years," Scientometrics, Springer;Akadémiai Kiadó, vol. 98(1), pages 577-582, January.
    • Handle: RePEc:spr:scient:v:98:y:2014:i:1:d:10.1007_s11192-013-1032-6
    DOI: 10.1007/s11192-013-1032-6
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11192-013-1032-6
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s11192-013-1032-6?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Samuel Arbesman, 2011. "Quantifying the ease of scientific discovery," Scientometrics, Springer;Akadémiai Kiadó, vol. 86(2), pages 245-250, February.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Vellasco-Gomes, Arianne & de Figueiredo Camargo, Rubens & Bruno-Alfonso, Alexys, 2020. "Energy bands and Wannier functions of the fractional Kronig-Penney model," Applied Mathematics and Computation, Elsevier, vol. 380(C).
    2. Zaheer Masood & Muhammad Asif Zahoor Raja & Naveed Ishtiaq Chaudhary & Khalid Mehmood Cheema & Ahmad H. Milyani, 2021. "Fractional Dynamics of Stuxnet Virus Propagation in Industrial Control Systems," Mathematics, MDPI, vol. 9(17), pages 1-27, September.
    3. Gauhar Rahman & Kottakkaran Sooppy Nisar & Thabet Abdeljawad, 2020. "Tempered Fractional Integral Inequalities for Convex Functions," Mathematics, MDPI, vol. 8(4), pages 1-12, April.
    4. Vasily E. Tarasov, 2021. "Integral Equations of Non-Integer Orders and Discrete Maps with Memory," Mathematics, MDPI, vol. 9(11), pages 1-12, May.
    5. Vasily E. Tarasov, 2019. "On History of Mathematical Economics: Application of Fractional Calculus," Mathematics, MDPI, vol. 7(6), pages 1-28, June.
    6. Tarasov, Vasily E., 2020. "Fractional econophysics: Market price dynamics with memory effects," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 557(C).
    7. Vasily E. Tarasov, 2019. "Rules for Fractional-Dynamic Generalizations: Difficulties of Constructing Fractional Dynamic Models," Mathematics, MDPI, vol. 7(6), pages 1-50, June.
    8. Vasily E. Tarasov, 2022. "General Non-Local Continuum Mechanics: Derivation of Balance Equations," Mathematics, MDPI, vol. 10(9), pages 1-43, April.
    9. Kottakkaran Sooppy Nisar, 2019. "Fractional Integrations of a Generalized Mittag-Leffler Type Function and Its Application," Mathematics, MDPI, vol. 7(12), pages 1-13, December.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Chung-Souk Han, 2011. "On the demographical changes of U.S. research doctorate awardees and corresponding trends in research fields," Scientometrics, Springer;Akadémiai Kiadó, vol. 89(3), pages 845-865, December.
    2. Jay Bhattacharya & Mikko Packalen, 2020. "Stagnation and Scientific Incentives," NBER Working Papers 26752, National Bureau of Economic Research, Inc.
    3. Michael Park & Erin Leahey & Russell Funk, 2021. "The decline of disruptive science and technology," Papers 2106.11184, arXiv.org, revised Jul 2022.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:scient:v:98:y:2014:i:1:d:10.1007_s11192-013-1032-6. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.