[go: up one dir, main page]
Skip to main content
Springer Nature Link
Log in

The Fractional-Order Backward-Difference of a Product of Two Discrete-Variable Functions (Discrete Fractional Leibnitz Rule)

  • Conference paper
Advances in Modelling and Control of Non-integer-Order Systems

Part of the book series: Lecture Notes in Electrical Engineering ((LNEE,volume 320))

  • 1246 Accesses

Abstract

In this paper a discrete fractional case of the so called Leibnitz Rule is presented The fractional-order backward difference of a product of two discrete-variable functions is derived. It is a generalisation to the first-order bacward difference of a product. The formula may be useful in the fractional-order backward differences of selected functions evaluation.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

References

  1. Ortegueira, M.D., Coito, F.: From Differences to Derivatives. Fractional Calculus & Applied analysis 7, 459–471 (2004)

    MathSciNet  Google Scholar 

  2. Kaczorek, T.: Selected Problems of Fractional Systems Theory. LNCIS, vol. 411. Springer, Berlin (2011)

    MATH  Google Scholar 

  3. Oldham, K.B., Spanier, J.: The Fractional Calculus. Academic Press, New York (1974)

    MATH  Google Scholar 

  4. Ostalczyk, P.: The non-integer difference of the discrete-time function and its application to the control system synthesis. I. J. System Science 31, 1551–1561 (2000)

    MATH  Google Scholar 

  5. Ostalczyk, P.: Discrete-variable Functions. A Series of Monographs Technical University of Lodz, Łódź (2001)

    Google Scholar 

  6. Ostaloup, A.: La dérivation non entière. Hermes, Paris (1994)

    Google Scholar 

  7. Podlubny, I.: Fractional Differential Equations. Academic Press, San Diego (1999)

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Applied Computer Science, Lodz University of Technology, ul. Stefanowskiego 18/22, 90-924, Lodz, Poland

    Piotr Ostalczyk

Authors
  1. Piotr Ostalczyk
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Piotr Ostalczyk .

Editor information

Editors and Affiliations

  1. Department of Electrical, Control and Computer Engineering, Opole University of Technology, Opole, Poland

    Krzysztof J. Latawiec

  2. Department of Electrical, Control and Computer Engineering, Opole University of Technology, Opole, Poland

    Marian Łukaniszyn

  3. Department of Electrical, Control and Computer Engineering, Opole University of Technology, Opole, Poland

    Rafał Stanisławski

Rights and permissions

Reprints and permissions

Copyright information

© 2015 Springer International Publishing Switzerland

About this paper

Cite this paper

Ostalczyk, P. (2015). The Fractional-Order Backward-Difference of a Product of Two Discrete-Variable Functions (Discrete Fractional Leibnitz Rule). In: Latawiec, K., Łukaniszyn, M., Stanisławski, R. (eds) Advances in Modelling and Control of Non-integer-Order Systems. Lecture Notes in Electrical Engineering, vol 320. Springer, Cham. https://doi.org/10.1007/978-3-319-09900-2_6

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-09900-2_6

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-09899-9

  • Online ISBN: 978-3-319-09900-2

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics