IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v12y2024i7p961-d1362864.html
   My bibliography  Save this article

Some Properties of the Functions Representable as Fractional Power Series

Author

Listed:
  • Ghiocel Groza

    (Department of Mathematics and Computer Science, Technical University of Civil Engineering Bucharest, Bd. Lacul Tei 124, Sector 2, 38RO-020396 Bucharest, Romania)

  • Marilena Jianu

    (Department of Mathematics and Computer Science, Technical University of Civil Engineering Bucharest, Bd. Lacul Tei 124, Sector 2, 38RO-020396 Bucharest, Romania)

  • Ion Mierluş-Mazilu

    (Department of Mathematics and Computer Science, Technical University of Civil Engineering Bucharest, Bd. Lacul Tei 124, Sector 2, 38RO-020396 Bucharest, Romania)

Abstract

The α -fractional power moduli series are introduced as a generalization of α -fractional power series and the structural properties of these series are investigated. Using the fractional Taylor’s formula, sufficient conditions for a function to be represented as an α -fractional power moduli series are established. Beyond theoretical formulations, a practical method to represent solutions to boundary value problems for fractional differential equations as α -fractional power series is discussed. Finally, α -analytic functions on an open interval I are defined, and it is shown that a non-constant function is α -analytic on I if and only if 1 / α is a positive integer and the function is real analytic on I .

Suggested Citation

  • Ghiocel Groza & Marilena Jianu & Ion Mierluş-Mazilu, 2024. "Some Properties of the Functions Representable as Fractional Power Series," Mathematics, MDPI, vol. 12(7), pages 1-13, March.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:7:p:961-:d:1362864
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/12/7/961/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/12/7/961/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Abeer A. Al-Nana & Iqbal M. Batiha & Shaher Momani, 2023. "A Numerical Approach for Dealing with Fractional Boundary Value Problems," Mathematics, MDPI, vol. 11(19), pages 1-12, September.
    Full references (including those not matched with items on IDEAS)

    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.

      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:gam:jmathe:v:12:y:2024:i:7:p:961-:d:1362864. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.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.