IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v250y2015icp665-674.html
   My bibliography  Save this article

On the classes of fractional order difference sequence spaces and their matrix transformations

Author

Listed:
  • Baliarsingh, P.
  • Dutta, S.

Abstract

The main purpose of the present article is to introduce the classes of generalized fractional order difference sequence spaces ℓ∞(Γ,Δα̃,p),c0(Γ,Δα̃,p) and c(Γ,Δα̃,p) by defining the fractional difference operator Δα̃xk=∑i=0∞(-1)iΓ(α̃+1)i!Γ(α̃-i+1)xk+i, where α̃ is a positive proper fraction and k∈N={1,2,3….}. Results concerning the linearity and various topological properties of these spaces are established and also the alpha-, beta-, gamma- and N-duals of these spaces are obtained. The matrix transformations from these classes into Maddox spaces are also characterized. Throughout the article we use the notation Γ(n) as the Gamma function of n, defined by an improper integral Γ(n)=∫0∞e-ttn-1dt, where n∉{0,-1,-2,…} and Γ(n+1)=nΓ(n).

Suggested Citation

  • Baliarsingh, P. & Dutta, S., 2015. "On the classes of fractional order difference sequence spaces and their matrix transformations," Applied Mathematics and Computation, Elsevier, vol. 250(C), pages 665-674.
    • Handle: RePEc:eee:apmaco:v:250:y:2015:i:c:p:665-674
    DOI: 10.1016/j.amc.2014.10.121
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300314014969
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2014.10.121?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.

    Citations

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


    Cited by:

    1. Ugur Kadak, 2015. "Generalized Lacunary Statistical Difference Sequence Spaces of Fractional Order," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2015, pages 1-6, October.

    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:eee:apmaco:v:250:y:2015:i:c:p:665-674. 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.

    We have no bibliographic references for this item. You can help adding them by using 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: Catherine Liu (email available below). General contact details of provider: https://www.journals.elsevier.com/applied-mathematics-and-computation .

    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.