IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v11y2023i13p3003-d1187729.html
   My bibliography  Save this article

Fractional Integrals and Derivatives: “True” versus “False”

Author

Listed:
  • Yuri Luchko

    (Department of Mathematics, Physics, and Chemistry, Berlin University of Applied Sciences and Technology, 13353 Berlin, Germany)

Abstract

Within the last few years, many of the efforts of the fractional calculus (FC) community have been directed towards clarifying the nature and essential properties of the operators known as fractional integrals and derivatives [...]

Suggested Citation

  • Yuri Luchko, 2023. "Fractional Integrals and Derivatives: “True” versus “False”," Mathematics, MDPI, vol. 11(13), pages 1-2, July.
  • Handle: RePEc:gam:jmathe:v:11:y:2023:i:13:p:3003-:d:1187729
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/11/13/3003/pdf
    Download Restriction: no

    File URL: https://www.mdpi.com/2227-7390/11/13/3003/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Jean-Philippe Aguilar & Jan Korbel & Nicolas Pesci, 2021. "On the Quantitative Properties of Some Market Models Involving Fractional Derivatives," Mathematics, MDPI, vol. 9(24), pages 1-24, December.
    2. Masahiro Yamamoto, 2022. "Fractional Calculus and Time-Fractional Differential Equations: Revisit and Construction of a Theory," Mathematics, MDPI, vol. 10(5), pages 1-55, February.
    3. Yuri Luchko, 2022. "Fractional Differential Equations with the General Fractional Derivatives of Arbitrary Order in the Riemann–Liouville Sense," Mathematics, MDPI, vol. 10(6), pages 1-24, March.
    4. Manuel D. Ortigueira, 2022. "A New Look at the Initial Condition Problem," Mathematics, MDPI, vol. 10(10), pages 1-17, May.
    5. Yuri Luchko, 2021. "General Fractional Integrals and Derivatives with the Sonine Kernels," Mathematics, MDPI, vol. 9(6), pages 1-17, March.
    6. Vasily E. Tarasov, 2022. "Fractional Dynamics with Depreciation and Obsolescence: Equations with Prabhakar Fractional Derivatives," Mathematics, MDPI, vol. 10(9), pages 1-34, May.
    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.
    1. Mohammed Al-Refai & Yuri Luchko, 2023. "The General Fractional Integrals and Derivatives on a Finite Interval," Mathematics, MDPI, vol. 11(4), pages 1-13, February.
    2. Vasily E. Tarasov, 2023. "General Fractional Calculus in Multi-Dimensional Space: Riesz Form," Mathematics, MDPI, vol. 11(7), pages 1-20, March.
    3. Vasily E. Tarasov, 2023. "Multi-Kernel General Fractional Calculus of Arbitrary Order," Mathematics, MDPI, vol. 11(7), pages 1-32, April.
    4. Tarasov, Vasily E., 2023. "Nonlocal statistical mechanics: General fractional Liouville equations and their solutions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 609(C).
    5. Maryam Al-Kandari & Latif A-M. Hanna & Yuri Luchko, 2022. "Operational Calculus for the General Fractional Derivatives of Arbitrary Order," Mathematics, MDPI, vol. 10(9), pages 1-17, May.
    6. Yuri Luchko, 2022. "Fractional Differential Equations with the General Fractional Derivatives of Arbitrary Order in the Riemann–Liouville Sense," Mathematics, MDPI, vol. 10(6), pages 1-24, March.
    7. Monica Aureliana Petcu & Liliana Ionescu-Feleaga & Bogdan-Ștefan Ionescu & Dumitru-Florin Moise, 2023. "A Decade for the Mathematics : Bibliometric Analysis of Mathematical Modeling in Economics, Ecology, and Environment," Mathematics, MDPI, vol. 11(2), pages 1-30, January.
    8. Muñoz-Vázquez, Aldo Jonathan & Martínez-Fuentes, Oscar & Fernández-Anaya, Guillermo, 2022. "Generalized PI control for robust stabilization of dynamical systems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 202(C), pages 22-35.
    9. Ravi P. Agarwal & Snezhana Hristova & Donal O’Regan, 2023. "Inequalities for Riemann–Liouville-Type Fractional Derivatives of Convex Lyapunov Functions and Applications to Stability Theory," Mathematics, MDPI, vol. 11(18), pages 1-23, September.
    10. Aldo Jonathan Muñoz-Vázquez & Guillermo Fernández-Anaya, 2024. "Uniformly Continuous Generalized Sliding Mode Control," Mathematics, MDPI, vol. 12(16), pages 1-19, August.
    11. Vasily E. Tarasov, 2023. "General Fractional Noether Theorem and Non-Holonomic Action Principle," Mathematics, MDPI, vol. 11(20), pages 1-35, October.
    12. Isah, Sunday Simon & Fernandez, Arran & Özarslan, Mehmet Ali, 2023. "On bivariate fractional calculus with general univariate analytic kernels," Chaos, Solitons & Fractals, Elsevier, vol. 171(C).
    13. Vasily E. Tarasov, 2022. "Fractional Dynamics with Depreciation and Obsolescence: Equations with Prabhakar Fractional Derivatives," Mathematics, MDPI, vol. 10(9), pages 1-34, May.
    14. Vasily E. Tarasov, 2022. "General Non-Local Continuum Mechanics: Derivation of Balance Equations," Mathematics, MDPI, vol. 10(9), pages 1-43, April.
    15. Vasily E. Tarasov, 2024. "General Fractional Economic Dynamics with Memory," Mathematics, MDPI, vol. 12(15), pages 1-24, August.

    More about this item

    Keywords

    n/a;

    Statistics

    Access and download statistics

    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:11:y:2023:i:13:p:3003-:d:1187729. 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.