IDEAS home Printed from https://ideas.repec.org/a/eee/matcom/v196y2022icp289-295.html
   My bibliography  Save this article

A note on a class of Caputo fractional differential equations with respect to another function

Author

Listed:
  • Zaky, M.A.
  • Hendy, A.S.
  • Suragan, D.

Abstract

The mathematical analysis and solutions for a class of ψ-Caputo fractional differential equations are discussed. Assuming that ψ(t) is strictly monotone and armed by the possibility of converting the ψ-Caputo fractional differential equations with respect to another function ψ to its Caputo counterpart by a mapping transformation, the solutions of the ψ-Caputo fractional differential equations can be deduced from the solution representation for the Caputo version via an inverse transformation. We show that the mapping transformation for such derivatives is extremely useful in practical applications. The representation of solutions for constant order time ψ-Caputo fractional diffusion equation and variable order ψ-Caputo fractional mobile-immobile diffusion equation is investigated and the regularity estimates are deduced accordingly.

Suggested Citation

  • Zaky, M.A. & Hendy, A.S. & Suragan, D., 2022. "A note on a class of Caputo fractional differential equations with respect to another function," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 196(C), pages 289-295.
    • Handle: RePEc:eee:matcom:v:196:y:2022:i:c:p:289-295
    DOI: 10.1016/j.matcom.2022.01.016
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378475422000283
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.matcom.2022.01.016?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.

    References listed on IDEAS

    as
    1. Restrepo, Joel E. & Ruzhansky, Michael & Suragan, Durvudkhan, 2021. "Explicit solutions for linear variable–coefficient fractional differential equations with respect to functions," Applied Mathematics and Computation, Elsevier, vol. 403(C).
    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. Pulido, M. Aurora P. & Sousa, J. Vanterler C. & de Oliveira, E. Capelas, 2024. "New discretization of ψ-Caputo fractional derivative and applications," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 221(C), pages 135-158.

    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. Fernandez, Arran & Restrepo, Joel E. & Suragan, Durvudkhan, 2022. "On linear fractional differential equations with variable coefficients," Applied Mathematics and Computation, Elsevier, vol. 432(C).
    2. Oscar Martínez-Fuentes & Fidel Meléndez-Vázquez & Guillermo Fernández-Anaya & José Francisco Gómez-Aguilar, 2021. "Analysis of Fractional-Order Nonlinear Dynamic Systems with General Analytic Kernels: Lyapunov Stability and Inequalities," Mathematics, MDPI, vol. 9(17), pages 1-29, August.
    3. Du, Feifei & Lu, Jun-Guo, 2021. "Explicit solutions and asymptotic behaviors of Caputo discrete fractional-order equations with variable coefficients," Chaos, Solitons & Fractals, Elsevier, vol. 153(P1).
    4. Restrepo, Joel E. & Suragan, Durvudkhan, 2021. "Hilfer-type fractional differential equations with variable coefficients," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).
    5. Irgashev, B.Yu., 2023. "Initial boundary value problem for a high-order equation with two lines of degeneracy with the Caputo derivative," Chaos, Solitons & Fractals, Elsevier, vol. 176(C).
    6. Fahad, Hafiz Muhammad & Fernandez, Arran, 2021. "Operational calculus for Caputo fractional calculus with respect to functions and the associated fractional differential equations," Applied Mathematics and Computation, Elsevier, vol. 409(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:eee:matcom:v:196:y:2022:i:c:p:289-295. 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: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/mathematics-and-computers-in-simulation/ .

    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.