IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v7y2019i8p707-d255266.html
   My bibliography  Save this article

On the Parametrization of Caputo-Type Fractional Differential Equations with Two-Point Nonlinear Boundary Conditions

Author

Listed:
  • Nazım I. Mahmudov

    (Department of Mathematics, Faculty of Art and Science, Eastern Mediterranean University, Famagusta 99628, T. R. North Cyprus, 10 Mersin, Turkey)

  • Sedef Emin

    (Department of Mathematics, Faculty of Art and Science, Eastern Mediterranean University, Famagusta 99628, T. R. North Cyprus, 10 Mersin, Turkey)

  • Sameer Bawanah

    (Department of Mathematics, Faculty of Art and Science, Eastern Mediterranean University, Famagusta 99628, T. R. North Cyprus, 10 Mersin, Turkey)

Abstract

In this paper, we offer a new approach of investigation and approximation of solutions of Caputo-type fractional differential equations under nonlinear boundary conditions. By using an appropriate parametrization technique, the original problem with nonlinear boundary conditions is reduced to the equivalent parametrized boundary-value problem with linear restrictions. To study the transformed problem, we construct a numerical-analytic scheme which is successful in relation to different types of two-point and multipoint linear boundary and nonlinear boundary conditions. Moreover, we give sufficient conditions of the uniform convergence of the successive approximations. Also, it is indicated that these successive approximations uniformly converge to a parametrized limit function and state the relationship of this limit function and exact solution. Finally, an example is presented to illustrate the theory.

Suggested Citation

  • Nazım I. Mahmudov & Sedef Emin & Sameer Bawanah, 2019. "On the Parametrization of Caputo-Type Fractional Differential Equations with Two-Point Nonlinear Boundary Conditions," Mathematics, MDPI, vol. 7(8), pages 1-23, August.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:8:p:707-:d:255266
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/7/8/707/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/7/8/707/
    Download Restriction: no
    ---><---

    Citations

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


    Cited by:

    1. Talib, Imran & Noor, Zulfiqar Ahmad & Hammouch, Zakia & Khalil, Hammad, 2022. "Compatibility of the Paraskevopoulos’s algorithm with operational matrices of Vieta–Lucas polynomials and applications," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 202(C), pages 442-463.

    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:7:y:2019:i:8:p:707-:d:255266. 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: 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.