IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v10y2022i19p3594-d931371.html
   My bibliography  Save this article

The Power Fractional Calculus: First Definitions and Properties with Applications to Power Fractional Differential Equations

Author

Listed:
  • El Mehdi Lotfi

    (Laboratory of Analysis, Modeling and Simulation (LAMS), Faculty of Sciences Ben M’sik, Hassan II University of Casablanca, Sidi Othman, Casablanca P.O. Box 7955, Morocco)

  • Houssine Zine

    (Center for Research and Development in Mathematics and Applications (CIDMA), Department of Mathematics, University of Aveiro, 3810-193 Aveiro, Portugal)

  • Delfim F. M. Torres

    (Center for Research and Development in Mathematics and Applications (CIDMA), Department of Mathematics, University of Aveiro, 3810-193 Aveiro, Portugal)

  • Noura Yousfi

    (Laboratory of Analysis, Modeling and Simulation (LAMS), Faculty of Sciences Ben M’sik, Hassan II University of Casablanca, Sidi Othman, Casablanca P.O. Box 7955, Morocco)

Abstract

Using the Laplace transform method and the convolution theorem, we introduce new and more general definitions for fractional operators with non-singular kernels, extending well-known concepts existing in the literature. The new operators are based on a generalization of the Mittag–Leffler function, characterized by the presence of a key parameter p . This power parameter p is important to enable researchers to choose an adequate notion of the derivative that properly represents the reality under study, to provide good mathematical models, and to predict future dynamic behaviors. The fundamental properties of the new operators are investigated and rigorously proved. As an application, we solve a Caputo and a Riemann–Liouville fractional differential equation.

Suggested Citation

  • El Mehdi Lotfi & Houssine Zine & Delfim F. M. Torres & Noura Yousfi, 2022. "The Power Fractional Calculus: First Definitions and Properties with Applications to Power Fractional Differential Equations," Mathematics, MDPI, vol. 10(19), pages 1-10, October.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:19:p:3594-:d:931371
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/10/19/3594/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/10/19/3594/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Ding, Liang & Luo, Yi & Lin, Yan & Huang, Yirong, 2021. "Revisiting the relations between Hurst exponent and fractional differencing parameter for long memory," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 566(C).
    2. Jianying Xiao & Yongtao Li, 2022. "Novel Synchronization Conditions for the Unified System of Multi-Dimension-Valued Neural Networks," Mathematics, MDPI, vol. 10(17), pages 1-24, August.
    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. Xiaojun Zhou & Chunna Zhao & Yaqun Huang, 2023. "A Deep Learning Optimizer Based on Grünwald–Letnikov Fractional Order Definition," Mathematics, MDPI, vol. 11(2), pages 1-15, January.
    2. Ragwa S. E. Alatwi & Abdulrahman F. Aljohani & Abdelhalim Ebaid & Hind K. Al-Jeaid, 2022. "Two Analytical Techniques for Fractional Differential Equations with Harmonic Terms via the Riemann–Liouville Definition," Mathematics, MDPI, vol. 10(23), pages 1-11, 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. Zeinali, Narges & Pourdarvish, Ahmad, 2022. "An entropy-based estimator of the Hurst exponent in fractional Brownian motion," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 591(C).
    2. Ren, Xiaohang & Xiao, Ya & Duan, Kun & Urquhart, Andrew, 2024. "Spillover effects between fossil energy and green markets: Evidence from informational inefficiency," Energy Economics, Elsevier, vol. 131(C).

    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:10:y:2022:i:19:p:3594-:d:931371. 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.